I went last year during the week of June 21st. lol.
Anyways, we (my grandma, mom and I) found it to be too hot. And we're from Minnesota so you'd think we'd be loving the hot weather. lol. But it was the damp, dry heat that we didn't like. Like you just feel gross cause it's so hot and icky. We still had a good time though.
The lines can get busy and have long wait times, but as far as I can remember the park didn't seem overly crowded or anything when we were walking around. So if that's the time you want to go, go for it. Just be prepared for some damp, sticky heat and long wait times at times.
I think it did rain a couple of times. I used to live in Florida for a month over in Miami and oh man. I swear it rained like ONCE everyday. This was in the month of July. It varies, but in the summer there's always a good chance of rain so be prepared for that as well.
Anyways, hope you have a great time.