Little thing, but it has a cumulative effect: always walk on the shady side of the path, if there is one. This will depend on what time of day it is, and what path you are on, but train yourself to pay attention and stay on the shady side.
Along with a mister fan that can hold ice, the washcloth/ziploc is a good idea. I prefer a flat cloth diaper to a washcloth. It's thinner and larger, so it can be tied around your neck, but still very absorbent, so it can hold a lot of water, if you like a "trickle" effect. The ziploc is doubly useful, as any counter-service outlet will give you ice for cooling purposes, but it is really helpful to them if you have something to put it in.
If you have kids with you, carry a change of clothes for them, so that they can play in the fountains. I always wear sport sandals, so I can splash a bit myself.
Re-apply sunscreen at least every hour, wear sunglasses and a hat with a BRIM!! (A baseball cap does not really cut it for keeping cool.)
Be aware of the signs of heat-related illness, and take it VERY seriously if you think anyone in your party is showing symptoms; heat problems can go from "just uncomfortable" to life-threatening in less than 10 minutes! If you feel sick from the heat, don't try to go all the way across the park to First Aid; go into any store and ask a CM to call the first aid center for you.
Here are some FAQ's from the CDC on this topic:
http://www.cdc.gov/nceh/hsb/extremeheat/FAQs.htm