Water cannot be emphasized enough, especially if you live in a much cooler climate. Make sure the kids have water containers at their sides at all times, and remind them to drink. Also, carry pieces of cloth that may be wet down and applied to pulse points for quick cooling. Lots of folks put a washcloth in a ziploc for this, but I prefer a flat cloth diaper, as it is thin enough to let air through, but also large and flexible enough to tie around the neck when wet.
Good sunscreen will help skin feel cooler, as part of the feeling of being hot is the "frying pan" feeling of your skin gently being cooked by UV rays. I recommend using sprays for most of the body, because they are quick to reapply often, and wax sticks for faces and ears, because the wax won't run into little eyes, and the stick is fun to use. Reapply at LEAST once an hour. (We reapply every time we stand in a ride line.)
Wear light-colored clothing whenever possible; it reflects heat rather than absorbing it. Also get broad-brimmed hats and sunglasses, and wear them all the time when outdoors. Make sure that your stroller has some sort of sunshade on it. Definitely bring surf shoes or waterproof sandals for everyone; the concrete in pool areas may be hot enough to burn, and with kids it is just easier to leave them in surf shoes at all times in those areas.
Try to plan your days so that you are out of the sun during the hottest part of the day, from about noon to 4 pm. We always go back to the resort for a swim and siesta during that time.
Heat-related illnesses are very serious business, make sure you know how to recognize them. Here is the CDC's page on heat illness. Please note the signs, as children won't always tell you when they are beginning to experience any of these, and especially not when they are excited:
http://www.cdc.gov/nceh/hsb/extremeheat/FAQs.htm
PS: I can't believe I forgot to mention mister-bottle fans. These help immensely, but make sure you get the sort with a large hole for ice. They sell them at the parks, but they are *much* cheaper offsite. Bed, Bath & Beyond nearly always has them in stock, even if you don't live in Florida.