Nothing wrong at all. Heat transference is part of having the ductwork in youd cabinets. It us what it is in a small kitchen with limited options. Don't store perishables in those cabinets.

make sure they actually put in duct work directing the heat out to the toe kick. my builder just left a hole in the floor and a vent in the toe kick. absolutely zero duct work directing the heat to the vent so the heat would hit the bottom of the cabinet and it would get super warm in there. we rigged up something directing the heat and it helped tremendously

Did they do anything wrong during heat duct installation to cause this?

I suspect there is no duct connecting the supply and the grille on the toe kick. The bottom of the cabinet is acting as the supply duct. That is a bad practice in my opinion.

They could have installed a Toe ductor when the base cabinet was installed. It is simple and costs less than $100 in materials. You could try installing a piece of rigid insulation to reduce the heat transfer. If other option is to cut open the bottom of the cabinet and install a duct between the supply and toe kick. A new sheet of plywood can then be added to cover the opening.

If there is a way to vent the heat there should not be an issue.

I agree you should figure out what he did to get the heat under the cabinet I have done this many times and the cabinet get a bit warmer than the ones without the duct but not so much it would spoil anything. Sorry but an actul kitchen installer should have been used not some random construction worker. Take the toe kick vent off and see what is behind it.

I had a toe register in my last kitchen. A great place to have dough rise! :-)

Pictures might help.
I’ve been considering toe kick heaters and now I’m worried…

Thanks for all the helpful suggestions.

There is a vent like the one in the picture under white cabinets in BeverlyFLADeziner's answer.

The construction workers are kitchen and bathroom installers and sent by a reputable home store where we got the cabinets from.

I checked the temp with a room thermometer and the cabinet directly above the heat vent was 82F and the ones near it 77F.

Did they insulate the ducting with that reflective wrap? Or even put foam around the ducting? This would have been my preferred method of installation. Anything to help prevent as much heat transference as possible.

Sweet stuff- did they put a metal duct in to direct the air to the new vent or did they just use the cavity under the cabinets as the duct?

Thats why I mentioned taking the front off to see what is back there

@mike_home Many thanks for the link, just what I've been looking for.

First, use a flashlight to see if there is ductwork, you may need to remove the grill. It is pretty common for people to treat any enclosure like ductwork. If there is no ductwork contact the company and discuss solutions with them.

If there is ductwork it likely needs to wrapped with insulation and so the cabinets should be removed and the duct wrapped. If you can't remove the cabinets lining the bottom of the cabinet with ductboard or some rigid foam insulation will help although it is an inelegant solution.

If there is no ductwork, you can add ductboard under the cabinets by piecing it in through the vent opening and gluing it to the cabinet. It will be a tedious and annoying job but will improve the problem.

ETA: to piece in ductboard measure a piece that fits exactly into your inside cabinet bottom. Shorten it for the toe kick (typically 3.75") then cut it in half. Apply adhesive to each piece and feed them in and adhere them. Use a broom handle to ensure they are adhered. If you want to add sides, cut them to fit (Usually 3" if you are using a 1" ductboard) and adhere them to the sides.

I checked the temp with a room thermometer and the cabinet directly above the heat vent was 82F and the ones near it 77F.

Given these temperature reading I suspect either there is no duct connected to the toe kick grille, or the duct connection disconnected during the installation of the cabinet. This is unacceptable in my opinion and the cabinet installers need to fix it properly.

Building Inspectors where I am require a duct all the way to the face of the toe kick- using the cavity as the duct is no longer acceptable.

Building inspectors where I am from seem to permit anything. The plumbing inspector here asked me three questions over the phone and asked me to text him a couple of pics so he could send me a sticker.

Thanks all for the suggestions.

There is a metal duct that connects to a wooden extension and then the vent.

What is a reflective wrap?

Reflective wrap is shiny bubble wrap that reflects heat.

Sweet - what did you end up doing? I have similar problem in my bath. The vent is in the toe kick of the vanity and the cabinets under the sinks and the drawers are too warm to store toilitries. The bedroom heat is also a problem - bedroom is hot and the rest of the house is cool.

I had this same issue with my bathroom and kitchen vents. Theres a video tutorial of how to fix it for free. I’ll add the link if I can find it. My caninets no longer cook my soap, water, and garbage bags 🤣

Here’s the video - How to fix cabinet vent missing duct work: https://youtu.be/K340kAcRqOs

Here’s an image of the video and item they teach you to make. I built the second option they show. It works really well!