Ways to store root vegetables in hot-humid climates??

I'm sure this question has been asked before but my searches haven't been very helpful so far. I'm trying to figure out how I can store a fairly large amount of root vegetables for a period of time (couple months maybe) here in Florida.
Any kind of under-ground structure is out of the question, unless it is absolutely water-tight, due to our high water tables. Someday I might try to take that on, but not today.
My house isn't the best place as we like it warm and we keep the temperature around 75-78F year round. We have a detached garage that might work alright in the cooler months but the temperatures fluctuate wildly here and there isn't much in the way of insulation in the garage.

Right now, the idea that is in the top of my mind is my tool shed/well house. It's got built in, sturdy shelves on the entire length of one of the walls, perfect for heavy vegetables/canned goods. Only issue I see is the temperature variation and the extreme heat in summer. I could add some insulation and a window AC unit. The AC might dry the air a bit but it's so humid here, plus the well tends to make it extra humid in there, it might actually be a benefit. I'm sure I could find a way to add some moisture if need-be anyways. Anything else I'm overlooking? Does this sound economical/feasible? Would there be a better way to cool this space? A better idea altogether?

I also have an attached garage that isn't currently connected to the AC system. It wouldn't be too hard to route the AC to it (the unit is 10ft from the garage) but it would still only make it 75-78F in there. I could add a window unit to cool it off even further but it would be about twice as much space to cool than the shed.

Any input would be greatly appreciated!

I'd try to find an old freezer to use as an above ground root cellar.

Freezers tend to have better insulation than fridges, so they work better with no extra insulation added.

If you add a layer of insulation to the exterior, you can have a really good root cellar in an old freezer.
either type (upright or chest) work but I prefer the chest type for this.

Would it be cool enough though? Insulation only really helps keep temperature in for so long. If the ambient temperature is 78, without any added cooling, the fridge would end up being 78 too. I was under the impression that the ideal temperature was around 60 for longish-term storage. Might be good for winter, outside or in the garage but what about the warmer months? We really only have a few months where the temperatures are consistently 60s or lower...

Our root cellar plans call for an ambient temperature of 48 f.

When I lived in Pensacola while stationed at the NAS, I used an old chest freezer for a root cellar.
As long as you aren't getting into it every day, it will stay cool once it has been cooled to your desired temp.

I wrapped mine in pink insulation covered with a sheet of plastic to hold it tight to the outside of the box.
I used 1" thick Styrofoam insulation on the lid since I could glue that to the lid for easy opening and closing.
I usually got into it once a week. When I needed to I would add a bag of ice in a bucket to cool the interior since where I had it sitting, there was no electricity available without running a long extension cord.

It might be worth a try if you can find one for free.

This may sound stupid, but can they be stored as living roots in the ground where they grow? This is how I typically store most root crops, except for short periods when I harvest too many to eat and put them in the fridge. This assumes a growing space large enough to leave crops standing, but root crops don't take up much space.

Yea, I'll def give it a try. People are always giving fridges/freezers away on Craigslist.

It's too warm to leave stuff in the ground here. I was trying to leave my carrots as long as possible but they started cracking and rotting :/ might work fine when it's cooler though...

our heat and humidity in Arkansas is very close to Florida weather types.

I have plans to dig a fairly deep root cellar, when ever it is that I can get to that project.

since you have some space under a roof, I think with proper planning and preparation you will succeed.

To store root vegetables you must maintain temperature between 34 and 40 degrees Fahrenheit with 95% humidity. The well house could be insulated and a window a/c installed cool the room. Another option would be to create a well insulated walk-in closet in the garage with a window a/c. The lower to the ground the cooler they'll be but you don't want to have them touch the ground. So pack them loosely in sawdust or peat moss inside a cardboard or wooden box sitting on top of 2x4's or a pallet.