I just got back from a very brief trip with only two park days. The heat was pretty brutal both days, but we found that it is much more manageable at Epcot than MK. All of Epcot's attractions are indoors, and Future World's are not spread out too terribly far. It seems like you don't go very far before reaching some shade and/or a shop or something with the doors wide open and AC pouring out. You could go into the Land pavilion, ride Soarin' and Living with the Land and then have a meal at Sunshine Seasons and literally be in there for an hour or more. The Seas pavilion has the Nemo ride and Turtle Talk, plus you can just wander around and look at the fish. Over at the Imagination pavilion you can ride Figment then go around the corner and do the Pixar film festival, which is a nice break. Around the World Showcase you've got the pyramid in Mexico with the Gran Fiesta boat ride and the little marketplace to explore. Also, if you want to eat lunch at La Cantina de San Angel (Mexico's quick service), they do offer indoor seating for lunch in the La Hacienda de San Angel restaurant (at least they did when we were there). The American Adventure show is long and has comfy seating, and you can sit on a bench in the rotunda for a break while waiting for Voices of Liberty. France's movie is seated and a nice respite from the heat.
We basically didn't feel overwhelmed by the heat at all at Epcot, and we were there from rope drop until closing.
Now Magic Kingdom is another story. The others have mentioned the best choices. We left the park and took the boat to the Grand Floridian. If you're interested in a quieter quick service and nice escape from the heat and hectic crowds of MK, take a boat to the Grand and eat lunch at Gasparilla's. Then go explore the lobby, there are a few shops or you can just sit on one of the couches and relax. We actually found a nice little quiet place up on the second floor where Citricos is. There are tables at Citricos' lounge area. We sat at one of those, there was an outlet nearby and I charged my phone and there was a window overlooking the pool area. The place wasn't even open, so it was very quiet, one other person was at a table just messing on their phone.
I can't speak to Hollywood Studios much, but they have a lot of shows, so finding places to sit in the AC and relax should be fairly easy there.
Animal Kingdom, to me, is the hottest and most draining of the parks. I love it, but you walk yourself to death and it's so dang hot. Nemo, Lion King, and Bug's Life all come to mind. The bird show (now it's the Up bird show, I think) doesn't have AC, but it is shaded if I remember correctly. Sometimes just getting out of the sun does wonders.