
I went in the peak of the heat a couple of trips. Here's some tips on what worked for me:
Stay in the shade when you walk from place to place - crisscross the walkways if you need to. Over an 8 hour day in the parks, you'd be surprised how much sun exposure you can avoid.
Wear a hat with a brim. I hate hats, never owned one, finally broke down and agreed to try a baseball hat, and wow, what a difference! Now I always wear a light weight cotton baseball cap in a light color, and pull my ponytail through the back opening. Keeps hair off of my face and neck, and the sun off my face.
Wear good sunglasses. I prefer polarized lenses to cut out all the glare from the cement walkways and waterways.
Wear a hydration pack and take sips on it frequently. Mine has some secure pouches so I just carry what I can fit in there. I put my water bladder in the refrigerator overnight and during all my room breaks. The water stayed nice and cool for a long time, and kept my back cool!
Dress appropriately. I have sleeveless, moisture-wicking, breathable tops, and lightweight nylon shorts that are quick-drying. I am going back this July/August, and am going to invest in some wicking, quick drying sports bras, too. I usually change mid-day or before we go back out again in the evening, if we can. There's something about a shower and a fresh change of clothes that makes you feel so much better in the heat.
Get into all the misters, interactive fountains, and on all the water rides you can. Buy a cup of ice from a counter service restaurant and rub it all over yourself. Stick some down your loved ones' pants. Makes the queues much more fun.
Wear open shoes. I use waterproof "Pretty Leather" Tevas. My husband has a pair, now, too. Same shoe, doesn't have "Pretty" in the name, lol, but it's the same shoe with a couple more manly looking details. I tried going in socks and sneakers one day in July and just about keeled over. The open feet makes a huge difference to me.
You'll never appreciate It's a Small World, Carousel of Progress, Hall of Presidents, Ellen's Energy Adventure, American Adventure, etc. more! Anything over 20 minutes where you sit in a/c will become your new favorite attraction.
Spend the high heat of the day (1 to 3 p.m.) at your resort in the pool or napping in your room.
Skip the big sit down dinners and use any time after the sun starts to sink to tour the parks. It'll still be muggy but you won't have the sun beating down on you.
Finally... sunscreen, sunscreen, and more sunscreen! That includes some kind of lip balm with sunscreen in it, too.