Salads! I grew up in the midwest with 100 degree temps and 80% humidity or higher. When it was really hot, my mom would have make your own salad night. She would set out lettuce, chopped tomatoes, cucumbers, peppers, carrots, celery and whatever other veggies were on hand, along with ham and turkey lunch meat, and shredded cheese. Sometimes she would also boil some eggs (although this does involve running the stovetop, so you might want to skip the eggs). Then everyone would make up their own salad with whatever they wanted. So long as you stick with lean meats and low-fat cheese (non-fat feta has only 30 calories per serving, you could always get something different for the kids if feta is too strong for them), this should be a fairly low calorie meal. Just make sure to go easy on the dressing or use a low calorie dressing and don't overdo it on the portions of meat and cheese.
As kids, we were really into this--it was always a special treat.
There is also a thread with some great salad ideas in the the Foods forum: What's your favorite salad?