I don't do very well in the heat either (and I'm from the South
). My tricks for keeping cool:
Stay well hydrated. WDW gives you free cups of ice water at the CS (anywhere there is a soda machine)
Stay away from sodas, tea or anything else w/ caffeine. (Caffeine dehydrates the body)
Wear a hat. It may seem hot, but it actually helps keep your head cooler.
Get one of those neck cool things(?). (I don't know the name of them, but you soak them in water and they expand (silicone inside); you put it around your neck and it keeps you cool)
I don't like the feel of the above mentioned neck cool things, so I use a bandana. I get it wet and wear it around my neck.
Take as many breaks from the heat as you can. Go inside buildings w/ AC and cool down you body.
Ride water rides (Splash Mountain, Kali River Rapids)
I usually have short hair, so I will get my hair wet in the middle of the day (really cools down the body)
Drink lots of ice water (free at WDW)
I can't think of anything else right now.