Definitely August. We were there this past August, and it was a great time to go. It had entered into the value season, so the rates on the resorts were lower. The crowds were lessened, due to the fact that many of the local kids were back in school, as well as those attending schools in the southern states.
Yes, it was hot, but with doing early morning touring, and taking breaks during the middle of the day, it was not intolerable.
Yes, it did rain, but many of WDW's attractions are indoors, and with umbrellas and a sense of humor touring wasn't bad at all... and it cooled things off.
That being said, you could pay me to be a guest at WDW during Easter (been there, done that... never again... wall to wall people, and not enough time to see even half of what you would see at other times). July is crowded as well.
As for how hot... mid 90's with humidity in the 90's, but it is tolerable, if you do it right!
Park hours for August: Epcot 9-9, MGM-9-8, AK: 9-5 and MK varies depending on night, but at that time, usually 9-6 or 7 with later hours on the weekends.
Remember to take full advantage of Magic Hours in the mornings, which are as follows:
Sunday: MK
Monday: AK
Tuesday: MGM
Wed: Epcot
Thurs: MK
Fri: AK
Sat: MGM
and if E ticket nights are offered at that time in the MK, they make for cooler touring and a way to do the big headliner rides when it isn't as crowded, hot and when MK is lit up!~
Glad you decided on August... you won't be disappointed!