One of the reasons I never refrigerate my cakes. If they're kept at room temp. humidity isn't a problem. It is very hot and humid here as well. The only time I had issues with a cake is when I put it in the refrigerator.
Air conditioning.
Sorry, that's the only thing I've found that works. I just did figures with a 50/50 mix of gumpaste and fondant. I tried putting them in front of a window air conditioner (didn't work that great), under a lamp (worked a little better), and finally in an oven with just the oven light on. The oven worked well for drying but they started getting soft again as soon as I took them out and back into the heat and humidity.
It might help some to add tylose or gum-tex to your fondant if you are using it to cover a cake. Hopefully someone with better advice will come along soon to help.
If you're talking about figures....I use 50/50 gumpaste/fondant or all gumpaste. I also put them in the oven (COLD) with the light on like cheatize said. 
I'm sorry about my first post I thought you meant the fondant on your cake being a problem. 
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