Staying at an on-property Disney hotel is a good start. You can commute to the parks in air-conditioned comfort using Disney bus, monorail or water transportation. This is definitely a better choice than driving a car that has been baking in the sun for hours.
Another incentive for staying on a Disney property is that you can take advantage of the Extra Magic Hour. On designated days, a Walt Disney World theme park will open an hour early for Disney Resort guests only. With that extra hour, you have time to take a break during the afternoon for a swim or a nap. Some resorts even have water activities, such as water skiing and surfing lessons, which are perfect for a hot day.
Pack a few water-mister fans. These little gizmo's are life-savers. It’s fun to buy the Mickey version in the park, but why pay $15 a pop if you can get them at Wal-Mart for $4.95 each? Kids will be fighting over them, so getting a few of them cheaply and packing additional batteries to go is a smart choice.
If you have a Park-Hopper Pass, cool down by visiting the water parks. Both Blizzard Beach and Typhoon Lagoon offer lots of fun for the whole family in the form of slides or raft rides. The water parks get crowded in a hot day pretty fast, so if you arrive at 11 am or after, expect plenty of queuing in the hot sun.
This is obvious, but crucial to mention nonetheless: dress light and wear sandals. Most theme-park guidebooks advise proper shoes and socks, but with the heat and humidity, wrapping your feet in socks isn’t actually going to help.
Remember to drink plenty of water. If someone in your group does get dehydrated, get to the First Aid Station. Each Disney theme park has one.
This is the best tip, which is why I’m saving it for the last. If you have tots, let them set the pace. Kids get cranky easily in the heat. This is more so considering that while you are looking at castles, they are in a hot stroller with nothing interesting at eye level. So if the kids are tired, head to somewhere with air-conditioning, have a break in a restaurant, or do anything that allows everyone to cool down.