For the last 10 years, we've gone to Disney for 7 days the first week after our schools let out, therefore typically anywhere from the 4th-14th. During this period crowds are still manageable because northern schools haven't let out and the true summer heat hasn't set in yet. It's still warm during this early June but the high humidity hasn't set in yet and this year was just like that and the crowds were way down compared to last year.
Now, you can read all of the archived weather info, but nothing prepared people for the heat wave FLA just had, nor the early rain in May. At home, from Fri-Mon we broke record highs in many cities and counties, and finally we've had enough rain in the last 2 days to bring things back to the normal summer heat, it's been unbearable.
Late June, July and Aug are brutal, but you should be able to count on mid day storms to cool things off a bit, but the humidity will be a toughy!
I live in Florida so we have no choice but to endure. We love Disney which is why we bought into
DVC, even if we're only 2 1/2hours away, we do EMH both am/pm, we work the Fastpass and we don't stay in the parks (unless it's TL day) between 12-4pm. I wish we could vacation in May maybe when he's in college!