I did a 1600 mile trip straight through without stopping except for gas. The car is comfortable, but just being in it that long started to bother me.
As for letting it cool down, I didn't, and you shouldn't have to. It's not like you're going to be pushing it to the max the whole time.
If you're low on gas by the time you hit Miami, gas up there. There is only one road into the keys, and there is no gas station until you hit key largo. Also, if you're there on the weekend, it will be packed and slow. All the weekend warriors head down there and cause a nice backup.