Hydration is the key--BEFORE the day starts as well as during the activity. There are a lot of great points listed on this thread. Here are some guidelines for beating heat-related illness from the American Academy of Pediatrics Committee on Sports Medicine:
Hydration: Plenty of fluids before and during exercise. A 90-pound individual should have 4 to 6 ounces of fluids EVERY FIFTEEN MINUTES (you can do the math for bigger girls). Water is fine, and sports drinks may actually stimulate more thirst. No fruit juices or sodas, no salt tablets.
Environment: SHADE (out of the direct sun as much as possible) as has been mentioned here several times.
Clothing: lightweight, breathable, with as much skin exposed as modestly possible to help with evaporation of sweat. A hat/visor can help too.
Acclimatization: practices for the first few weeks of hot, humid weather should start light and gradually increase in intensity. This can help players get used to playing in the heat.
Medical Conditions: know of any medical conditions of your players--keep close tabs on heavier players as they are more susceptible to heat illness. Players should avoid cold medications (can keep a person from getting rid of heat).
Whenever a player feels confused, dizzy, nauseated, sleepy, or otherwise ill while playing in hot weather--you have to consider heat illness. Get that kid drinking right away and in a cool them down (can use ice if necessary)--if they don't start getting better, send them to the emergency room right away.
As Johnnies mentioned, Pedialyte is a good re-hydrating solution (it also tastes like sweat, so that's another reason girls may not like it). Water is probably the best overall as it is readily available.
When playing in this heat, I always try to tell my daughters that when they urinate it should look like weak lemonade. If it looks like apple juice, they are not getting enough fluids and need to drink a lot more.
Now, if the rains stop maybe we can get out and play this weekend!