Mini split would be the cheapest, if the unit freezes up it's more to do with refrigerant leaks, lack of maintenance, bad blower motor. The other is if you run it when the temp outside is below 55F degrees. (The outdoor ambient temp can be over come, but this requires extra work and knowledge -- your climate in Hawaii this shouldn't be a big problem)

If you decide on the mini split option, you would want one that has a dry mode and is an inverter model. Sizing is more critical for this type of application. So keep that in mind.

But in terms of what you *really need* it's called a humidor. That is a specialty market, so it's likely to cost more than the mini split option --- because the company you choose to do it, will custom design it for the space and climate concerns.

Here's a link to a Custom Humidors & Wine Cellars for some more insight.

If you're putting expensive wine in there, probably worth the extra money to do this right, spend the extra money on a custom designed humidor.

If the rest of the home has central AC, and you keep it running, then over supplying that one room with a big duct ought to get you there most of the time, How close, and how precise are you willing to pay for is the question.

The humidity level in a humidor is too high for food storage.

Sounds like you need a unit that would be used in a small walk-in cooler like a restaurant. They very often reject their heat to the space they're in and not the outside. An alternative could be a very small window unit. At the temperatures you are planning it wouldn't run much.

Thank you everyone for your responses! Austin, I met with an HVAC company today and they recommended to install a 6,000 BTU mini split (ductless) unit inside the tiny room. They said it will operate fine despite the room being 80% smaller than a room the unit was designed for. I remeasured the room and it's actually 5x5x8. They did say if the exterior temperature where the condenser is located reached over 85 degrees, the unit may not be able to maintain a constant 65 degrees. The technician said that the max temperature drop is generally about 20 degrees. So if it's 90 degrees outside, the max cold inside the room would be 70 degrees. That didn't make sense to me because the room was so small relative to the BTU output of the unit but perhaps this is a limitation of mini splits? Does this seem accurate? A humidor is not an option because I need the room to be as dry as possible. The room is primarily for food storage, wine is secondary. I have read that as long as wine stays in the 65-70 degree range, it should not spoil. And that it's not necessary to preserve or "age" wine at 55-60 degrees. You just need to drink the wine within several years of their release and that is always the case in our household. Thank you again for your replies.

Ok so wine storage is a tricky thing. I decided to search for some clarification as to what's needed and what would be considered 'over kill'.

Snippets of information below taken from here:

1. Keep it cool

Heat is enemy number one for wine. Temperatures higher than 70° F will age a wine more quickly than is usually desirable. And if it gets much hotter, your wine may get “cooked,” resulting in flat aromas and flavors. The ideal temperature range is between 45° F and 65° F (and 55° F is often cited as close to perfect), though this isn’t an exact science. Don’t fret too much if your storage runs a couple degrees warmer, as long as you’re opening the bottles within a few years from their release.

2. But not too cool

Keeping wines in your household refrigerator is fine for up to a couple months, but it’s not a good bet for the longer term. The average fridge temperature falls well below 45° F to safely store perishable foods, and the lack of moisture could eventually dry out corks, which might allow air to seep into the bottles and damage the wine. Also, don’t keep your wine somewhere it could freeze (an unheated garage in winter, forgotten for hours in the freezer). If the liquid starts turning to ice, it could expand enough to push the cork out.

3. Steady as she goes

More important than worrying about achieving a perfect 55° F is avoiding the landmines of rapid, extreme or frequent temperature swings. On top of cooked flavors, the expansion and contraction of the liquid inside the bottle might push the cork out or cause seepage. Aim for consistency, but don’t get paranoid about minor temperature fluctuations; wines may see worse in transit from the winery to the store. (Even if heat has caused wine to seep out past the cork, that doesn’t always mean the wine is ruined. There’s no way to know until you open it—it could still be delicious.)

4. Turn the lights off

Light, especially sunlight, can pose a potential problem for long-term storage. The sun’s UV rays can degrade and prematurely age wine. One of the reasons why vintners use colored glass bottles? They’re like sunglasses for wine. Light from household bulbs probably won’t damage the wine itself, but can fade your labels in the long run. Incandescent bulbs may be a bit safer than fluorescent bulbs, which do emit very small amounts of ultraviolet light.

5. Don't sweat the humidity

Conventional wisdom says that wines should be stored at an ideal humidity level of 70 percent. The theory goes that dry air will dry out the corks, which would let air into the bottle and spoil the wine. Yes, this does happen, but unless you live in a desert or in arctic conditions, it probably won’t happen to you. (Or if you’re laying down bottles for 10 or more years, but then we’re back to the matter of professional storage.) Anywhere between 50 percent and 80 percent humidity is considered safe, and placing a pan of water in your storage area can improve conditions. Conversely, extremely damp conditions can promote mold. This won’t affect a properly sealed wine, but can damage the labels. A dehumidifier can fix that.

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So my first impression was the humidity control was more important and now after reading that information realize temperature is more important. Ideally 55 degrees. Avoid sudden fast temperature changes.

Humidity is less of a concern, except in the event corks dry out. So because you typically want a higher humidity with wine storage it may be better to separate that from the dry food. (You can purchase small wine coolers that are designed to store wine in, if you don't have a large storage of wine that is. That's an option to look into.)

Your goal to store wine at 65 may be too high. I'm not a wine storage expert so this information are things to consider.

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The difficulties in making this work with a mini split.

The small room in which this sits puts what ever system you choose to cool it at the disadvantage of load changes. A load in air conditioning or refrigeration for that matter is heat.

To expel that heat --- what ever heat there is to expel from the 'conditioned box' the appliance is more efficient when expelling heat to a cooler air temperature.

In other words a cooler air temperature will marginally increase the performance and capacity of the mini split. Because heat moves from hot to cold, much more freely than hot to hotter.

There is additional heat from the operation of compression that aids in this sequence. As the temperature outside increases there is less and less heat that can be expelled. This is primarily the reason AC equipment is sized for what is typically the hottest days / month of the year for a given climate.

If you try to compensate for this problem in your case upsize the unit to say 9000 BTU to alleviate a potential problem of a heat wave then the unit may be over sized the rest of the time and short cycle, because the load inside the conditioned box is low --- and the outdoor temp is cooler providing better thermal transfer.

Because you are trying to use a mini split outside of it's design specs there will be challenges to over come. It's a tough call here. If you can find a 9000 btu inverter mini split that lowest speed settings the unit can operate in 3000 btu capacity then that may be the better bet.

Inverter technology allows compressors to run extremely slow. This will limit short cycling. Short cycling is detrimental because it kills compressors, which can get expensive in a hurry.

Another option may be in how you control it. If it's cooler outside drop the temp inside the room to 55 forcing the cycles to be longer. The extra capacity of the 9000 btu mini split comes into play if temperatures get hotter out doors.

It really depends on the load in the box. I don't think there is any go between from 6000 to 9000 BTU sizes. So maybe ask your company what they think about a 9000 BTU mini split and dropping the temp a bit to say 55 or 60 degrees as a possible work around to the sizing issue.