Go the second or so week of June. For the last 2 years, we've gone then and it's perfect. The parks are starting to open later and run the night shows more often, but attendance is still moderate because many kiddies are still in school.
Also, you can usually find discount codes on sites like www.mousesavers.com for that time period. They really want people to come down then - I just got Port Orleans Riverside from June 6-12 for $89 a NIGHT! That's the discount for Disney Visa Card holders, and it's $55 off the rack rate!
I've been in August, July and June - and June is my favorite of the summer months!
Please please please remember to head back to your room for a nap and a break from the fun in the afternoon. Especially when the heat is awful. And when the party is refreshed, you can head back to the parks.