Have you ever looked into cooling vests?
I would really suggest you look into touring plans so that you can plan for going back and forth from indoor activities to outdoor activities and back to indoor ones again. Also, I find that that having a detailed touring plan keeps me from trying to do "just one more thing" over and over again as the day wears on and gets hotter and hotter; it reminds me to get my family out of the parks. You can go back in the evening when it's getting darker and cooling down.
An umbrella may also help as it'll keep the sun from beating down on you. Just be careful in crowds as most people at WDW really aren't paying much attention to where they're going and umbrellas are at some people's eye level.