We went around June 12-20 last year and we had a wonderful time. I was so worried before the trip b/c I don't like crowds and I don't like heat. True, it rained during the afternoon for most of the days. But, you just have to do some planning. We'd get to the parks at opening, stay til around 3 or 4 and go back to the resort and swim and relax and then go back to the parks during the evening. By the time we'd leave the parks at 3, the crowds WOULD be unbearable and it would usually look like a storm was coming on, but we'd be on our way out.
We used fastpasses, so we never waited in line more than 10-15 minutes, and we rode on everything. It was hot and sweaty, but we carried water bottles and drank lots of water. And it seemd like we were always walking into some air conditioned attraction. I don't remember feeling that uncomfortable. The plus sides to the crowds and heat were that the pool was so warm and yet it felt great, and the parks are open so late.
We're going Easter week this year (from Easter Monday evening til the following weekend). I keep hearing the crowds are even worse, but I think we'll be able to deal with it.
You'll have a magical time!!