What color are your containers? Paint them white if they aren't. I don't think ice cubes would do much unless they were pretty big cubes. Maybe if you put your trees into a larger container and put ice between the two containers but that would still melt awfully quick in 100+ temps.

Instead of cubes I would freeze some plastic bottles of water and place them around the plant. Fuji sells water in square containers, which are easier to nest. Although cases of small bottles of water at CostCo are more cost effective.

Cover, better yet completely drape, with an insulated blanket or old sleeping bag. Try GoodWill if you don't have an old sleeping bag to dedicate to this cause.

Another idea is those folding reflective windshield thingies for your car. Bungee cord it around the containers, then add the ice bottles. GL with it all Travis.

Shade cloth suspended above plants. Lets in some light but cuts it back quite a bit.

It's 110° or more here. We need more than shade cloth. The only plants in my garden that are happy are the chili peppers.

Ice cubes to keep container trees cool? I've never put that particular strategy to work, but I have seen it utilized many times for trees on display at bonsai shows. All considered answers should give some consideration to whether or not the plant whose medium you're trying to keep cool actually needs water. Arranging ice cubes on the soil surface of a potting which already has several inches of perched water in the pot is going to add to the counter-productive effects of over-watering. So, in some cases it might not be a realistic approach to keeping actual root temperatures below 90*, which is often used as the temperature at which root function begins to be seriously limited for a very high % of trees.

Root damage from high temperatures is a serious matter that very often escapes notice, or at least escapes diagnosis. Something experienced bonsai practitioners understand is the effects might not be seen for as long as a month or two after the damage is done. Typically, the worst damage is on the side of the pot that gets the most sun exposure from midday until evening. When the symptoms of the damage appear, they are usually made manifest in branches on the side of the damage simply closing up shop and dying, or even loss of viability of the entire side of a tree. Unfortunately, the rotting roots provide an easy pathway by which fungal infections can spread systemically to all parts of the tree, often ending the tree's viability.

My grow benches are arranged so trees I know are sensitive to high root temperatures can be moved to the back (north) side of the bench, where pots on the lower shelf are shaded by the the upper level and foliage of those plants situated there. The root-over-rock plant with the green tape is on the south side of the poly plant it rests on, so on the entire 24 foot length of the north side, pots are shaded but foliage is or isn't depending on where the plant is placed on the plank. The take-away here is to provide shade for at least the pots when it's hot. Often, a 2x6 or 2x8 set on edge between the sun and a pot is all that's needed.

In summer, in order to help keep roots cool, I try to water in mid-afternoon - around 2 PM. This cools roots immediately, and the fact that the entire soil column will have been soaked increases evaporative cooling. I also have a significant advantage over most growers of containerized trees in that I use a highly aerated grow medium that holds virtually no excess water. This allows me to water at will without concern I might be over-watering. As I noted, the superior gas exchange afforded by well-aerated medium increases evaporative cooling, but the medium also allows me to water when the plants only need cooling and not a larger volume of water - a very big plus, from the plant's point of view. I run the hose until the water is cold (maybe 60-65*) and use a water breaker to ensure the entire soil column is moistened.

Masakuni water breaker ^^^ Works at very low to high pressure because of how fine the holes are.

That's the view from here. As always, YMMV.

Of all the solutions listed above, the best and most practical was the one made by Dave in No VA.

Very impressive Tapla. I like that setup.

Dave and Silica, You ever been to Phoenix in July/August? Try that first then you can weigh in on solutions.

Travis' trees are in pots, not in the ground. That makes a huge difference. He's in a rental or a strict HOA community therefore unable/unwilling to plant in the ground. When he gets his agri-lot, life will likely be much different. 120° for 2 or 3 days in a row is not unusual in high summer.

I appreciate the feedback here! MaryMcP is correct, my HOA is weird and won't allow citrus or fruit trees (!) so these guys are stuck in pots for the foreseeable future. I understand why adding some type of shade would be a top recommendation, but these are sitting under my front porch and are already in shade by about 1200-1300 (by intention), so I don't think the solution is to add shade (though how would anyone know this since I did not state that in my OP?). To Tapla's comments, I am growing in my best approximation of the 5-1-1, though I must still have a PWT because I cannot water with abandon (at least not my citrus). My question about ice cubes was not intended to increase watering, but to try and cool the roots so they could make use of the water already in th soil. I am intrigued that you water in the mid-afternoon as I thought it would be more efficient to water during the cool(er) hours when the roots would be more efficient at taking up the water. Perhaps I will shift my schedule so my watering can help cool the roots. My trees are on a drip system so the water is probably pretty warm when it first comes out. I water by hand on the weekend and I make sure to let the hose run for a bit first.
It's also interesting that Tapla mentioned reduced vigor as a consequence of heat damage. My Meyer is in its first season growing lemons, and all the lemons are on the back (shadier) side. I thought this odd because I expected more growth on the sunnier side. Fruit set before temps got out of hand here. Perhaps this is an indicator of heat damage on the front side.
FWIW, I sprayed the trees with kaolin clay for the first time this season. That definitely seems to help with sunburn. We never get rain in Phoenix but wouldn't you know it, it rained 1-2 weeks after I sprayed and now I need to reapply.

I forgot to comment on the other recommendations. Wrapping the pots in the reflective materials sounds effective but would not pass the wife approval test, and would surely catch the eye of my vigilante HOA. But I can certainly freeze some water bottles and place those on the container. That sounds more effective than some ice cubes.
I have a long term plan of building some large wood planters that I could place the pots in, and do a sort of pot-in-pot setup, I just didn't get around to it before summer set in this year. Put it on my tab....

MaryMcP Zone 8b - Phx AZ -- Then I would suggest switching out citrus plants with Fouquieria splendens or Carnegiea gigantea.

Mary McP, my question would be why on earth would you even consider living in a HOA area ?

That would be my question too Silica. I don't so you'll have to ask the OP'er, Travis that question. I've had trouble caving to authority since I was a kid and I'm in my 70's now. Doubt I'd be any better at it. :-)

Dave, I would love either of those alternatives! My wife finds the ocatillo less attractive than I do, but both would grow well here and blend in well :). Problem is neither produce the fragrant blossoms or desired fruit. So I will continue to hack away at with my citrus, at least for now.
Mary and Silica, This is our first home purchase. Initially we thought the HOA was a good thing because our neighborhood is manicured and attractive. I did not anticipate their landscape guidelines would be so prohibitive. As I look for the next home, I'm definitely more cautious about the HOA.

"My question about ice cubes was not intended to increase watering, but to try and cool the roots so they could make use of the water already in th soil. I am intrigued that you water in the mid-afternoon as I thought it would be more efficient to water during the cool(er) hours when the roots would be more efficient at taking up the water. Perhaps I will shift my schedule so my watering can help cool the roots." You were perfectly clear in conveying your concern is centered on keeping root temperatures from rising too high, I just wanted to be sure that you had considered the melting ice would increase the amount of water in the medium and would only provide a workable solution if the plant had dried down enough that you weren't exchanging the stress of high root temperatures for stress caused by an excessive amount of water in the pot.

High root temperatures, too much water in the medium, or too little water in the medium all cause specialized cells (guard cells) to shrink, which closes off stomata, the small openings in foliage through which water vapor and other gases move. This is how plants limit water loss as their internal water pressure (turgidity) decreases. Closed stomata limit evapotranspiration, a plant's ability to cool itself, so while the ice cubes are melting and lowering soil temperatures in the hope of increasing root function, any increasing excess of water in the medium will be limiting root function. So even if a decision is made re what foot you'll be shot in, it's still gonna hurt.

If you water in the cool hours of morning (and if you wet the foliage as you water), leaves will be dry before dark, which helps to limit fungal infections, so that IS a benefit of watering early. The downside of watering in the morning lies in reality that the top inch or two of the medium will likely be dry by the time the hottest part of the day comes around. When watering in early to mid-afternoon when it's hot, I avoid wetting the foliage of plants as I ensure the entire soil column is wet, which maximizes evaporative cooling. With enough moisture in the medium and enough gas exchange occurring, root/soil mass temps can lag ambient temps by as much as 15*.

BTW - fruit on only one side of the tree does first bring to mind a localized root issue. In many woody plants, veins of living transport tissue develop on the trunk. Junipers, arborvitae, yew are all known for their easily seen veins with direct relationship to individual branches. The muscular yew below and the juniper below that serves as witnesses. I don't know how direct the relationship is in citrus, but I do know that one-sided problems usually have one-sided causes.

^^^ In another 500 years, the sapwood and heartwood of this tree will have rotted away, leaving what the casual passerby would see as a clump of individual trees.

Al

If the ice was in a sealed container, it certainly would not ever enter the soil of the plant. Maybe wrap two or three hot water bottles filled with ice around the pot and place the whole thing within a larger pot with some insulation over the top. Of course, you'll need to refill each morning.

Larger bottles filed with ice, as Dave & Mary suggested, would certainly last longer than simple ice cubes.

Lots of good information here! Thanks Al and Dave (and those who posted before, Mary and Silica and Ken). I didn't think the melting ice cubes would add an appreciable amount of water, but it makes sense it would take an appreciable amount to have an appreciable cooling effect 😜.
I removed the mulch in these pots at the beginning of the season because I read a previous discussion by Al that suggested mulch, while helping to retain moisture, limited ability to cool roots/soil by evaporation. Since I'm more concerned about temperature than water availability, I figured I would try this out this summer. Being on a drip system, I can have it water mid afternoon without fear of wetting the foliage (though in this dry climate, I don't think my trees are at significant risk of fungal infection anyway). The water will likely be much warmer coming out of the drip tubes in the heat of the day, however. I do have them buried as much as possible, but I'm sure they still absorb heat.
My Meyer bloomed all over, but only the fruit on the shady side set. Interesting, I'll watch for more one-sided root issues.

Hi Dave, Just a quick clarification regarding my suggestion of frozen water bottles. You are right, most of the chill from the frozen bottles will simply gas off into the air. That's the purpose of the insulated blanket, it will allow the chill factor to remain under the insulation. You have provided some great tips and info. Appreciated. mm

What about something like this:
https://www.amazon.com/Swiss-Safe-Emergency-Blankets-Signature/dp/B0717143P2/ref=mp_s_a_1_17?dchild=1&keywords=insulating+blanket&qid=1625157213&sr=8-17&th=1&psc=1
It's pretty ugly but must of the ones I'm seeing are silver and I shudder to imagine how much light and heat would be reflected into the canopy.

Or maybe something like this:
https://www.amazon.com/Frost-King-CF1-Multi-Purpose-Insulation/dp/B004Y6SX1Y/ref=mp_s_a_1_5?dchild=1&keywords=insulation+blanket&pd_rd_r=44fdeb43-5803-4ecd-ba71-07dfbc10c48d&pd_rd_w=TDKMc&pd_rd_wg=QRFGx&pf_rd_p=ce028c81-ed8c-425a-8404-93bf425aa8ce&pf_rd_r=DF30DFBD2MQVJX8KXD9N&qid=1625157516&sr=8-5