I live in Phoenix, even hotter. If you want to keep your shirt tucked in, options are more limited. There are IWB holsters where the shirt can be tucked over the holster and still inside the pants. Mitch Rosen and Galco have these, I think, and there is the newer Versa-Carry minimalist approach.
There is the Smart Carry/Thunderwear approach where you carry down the front of your pants (!) with a separate bellyband-type holster. There is the classic style of bellyband, where your shirt I think would need to be looser, even if still tucked in.
It depends on your build whether IWB works or not. I have put on a bit too much weight and in the heat prefer something I can carry easily in the front pocket. Don't like having my gun carried behind the hip either, where I can't see whether it's showing or not. I suppose even a heavier person could buy bigger pants and still IWB.
Maybe take a look again at the various carry styles above to see which appeals to you. How you want to carry dictates, in part, what gun you would buy.
If you decide that front pocket or ankle carry is best for you, you are looking at a class of smaller and lighter guns than the classic metal-frame .380s that have caught your eye. These would generally take some practice to get used to shooting.
Consider for pocket carry the Smith Airweight revolvers (with or without holster), Ruger LC9 or the tiny LCP .380, the Kahr CM9, which is actually pleasant to shoot, and the Colt Mustang Pocketlite/SIG P238, which are also OK to shoot but are single action which you may not prefer. The Bersa Thunder 380 CC is bigger but still might work in a pocket without a holster.
I can vouch for the Bersa, the LCP and the Airweights, and most people like the Kahr CM9 though mine was finicky.