I second (or fourth or fifth or whatever

) the TTA, but the downside is that it's not really "air conditioned", so not the best choice on a hot day. The movement and shade do keep the ride cooler than out in the blazing sun but if you REALLY want to cool off, look elsewhere.
I too really like the upstairs room in the Columbia Harbour House. Not many people go upstairs - even during peak meal times when the downstairs is packed I'm usually one of the few people upstairs. And, of course, it's air conditioned and cool drinks are nearby.
If you're in Epcot, the obvious choice for cooling off is Ice Station Cool near Innoventions (West or east? the one on your right as you're entering the park. I think that's east, but not sure) - they give out free Coke products from around the world. Pretty refreshing! I like to bring my souvenir mug from the hotel and fill it up with a mixture of the China watermelon juice and something else, maybe from Vietnam or Thailand. The Asian ones are fruity. (DON'T try the Beverly from Italy, it's extremely bitter and has become quite notorious on these forums...)
Any of the theaters in MGM or Epcot are good choices.