You can also look at past years data, just do a google search for it.
I was just looking at June 1-10
High temp seems to be around mid to high 80's, but one year was solid 90's. Some rain almost daily, but almost never measurable. 80-100% humidity, but one year it was only 60%.
Long range weather centers show a fair amount of rain for the summer in that area. But rain is not really a problem in WDW, you just get wet...