Our last nine trips to WDW have been during the last week of May through the entire first week of June. Over the years, we have found that the crowds have gotten bigger but definitely not unmanageable.
The first weekend in June is Gay Days. The crowd levels are definitely effected by the extra guests. But, you can work your way around the extra crowds. The gay/lesbian travelers participating in Gay Days have a specific schedule they follow. You can probably find that over on the Gay/Lesbian forum. Usually, they are in the Magic Kindgom on Saturday so we make sure we avoid that park on that particular day. The Saturday crowds at Magic Kingdom are usually busy anyway and with the extra guests, it makes it even more crowded.
I don't know if the Star Wars Weekends have been scheduled yet but they do usually occur in June. To avoid those crowds, just avoid MGM Studios if possible.
With some advanced planning and the use of Fastpass, you will be able to see and do lots during the time period you are talking about.
We always arrive at park opening and stay until park closing. Although we don't leave the parks for a rest, we do make sure we do work in at least a couple of break times. Each of the theme parks have some quiet spots and we make full use of them. We also linger a while over our counter service lunches and make our table service ADRs for dinner. Table service dinners usually take about an hour to an hour and a half. By the end of our meal, we are rejuveniated and ready to head out again.
The temperatures do vary but, most of our visits, it was in the high 80's, low to mid 90's. We are from Louisiana and the high temps and high humidity didn't bother us that much since we are used to it. You can purchase the misting fans in al of the theme parks but we bring along our own since they are a bit pricey in the parks. I found small misting fans at our local Wal-Mart for $2.50. They are about the size of a small digital camera and have a clip on them. Because they are small, they don't get heavy and you can clip them to your belt loop.
Our next trip is scheduled for May 29th through June 7th, 2008 and we are already counting down the days!