We just got back (7/1 - 7/7), here are my thoughts:
Let me first say that this is comming from the perspective of someone with little ones in strollers. I'm sure if it was just adults, we would have been able to bear the heat better, but then again, maybe not.
Get to the parks as early as possible. We are not morning people and so on our first day, we strolled into MGM late morning and were only able to stand it for a couple of hours. We quickly became early risers.
When you start to feel like you can't cool off, leave the park. We pushed it one day and I felt like crap the rest of the day. I think in your case, just set a time and leave then. To me it seemed like by the time I started feeling really hot, it was too late and I couldn't avoid the headaches.
It starts to cool off around 5 or 6, but it's still humid. It's never going to be comfortable in July or August, but at night it does get a lot more bearable.
Here's something else... the park you are at has everything to do with the heat as well.
Magic Kingdom - There are many AC rides, so you can usually avoid the heat. Also, it has a lot of counter type restaurants to cool off in. We were able to speed all day there without having to leave.
MGM - A lot of AC rides as well. You can usually stick it out at MGM. I think the only bad thing is that the buildings and structures seem to reflect a lot of light and it always seemed very bright to me.
Animal Kingdom - Honestly, I wouldn't even bother with this park in the summer. It's too damn hot. We did the safari in the morning and left. It was PACKED at opening and hardly anything is indoors. The vegetation is sufficating. There are too few rides to spread the people out and most of the queue lines are at least partially, if not totally outdoors.
Epcot - I love this park in the summer. Everything is indoors. There are tons of places to just sit down in the AC and cool off. We spent an entire day there and hardly broke a sweat in 95 degree weather.
Fans and misters help, but won't completly beat the heat. Nothing will except to just leave the park and find some AC.
-Bill