I live in Virginia and have a superhuman sweat rate (seriously, it's my greatest talent). I love the post about praying for storms as in college I would sometimes time my runs to try and catch a t-storm blowing in (the breeze would feel phenomenol)! But that's not the safest thing so I don't necessarily reccomend it. Here's my advice...
1. As others have said you are battling three things - 1. straight up high temperatures, 2. unbearable humidity, and 3. hot sun. You should never really have to deal with #3 as going early or late takes care of it plus it's not that hard to find shady routes. For me humidity was always much worse than higher temperatures (because it would make me sweat so much) so I do most of my running later than 6:00 at night and it's really hot closer to 7 or 8. It's not bad while you're out there.* But if the humidity doesn't bother you so much then I would say start your runs before 8 in the morning. I think that's best because it give you the whole day to recover.
*The problem with running at 7:00 at night is after 10 miles in still hot conditions you're pretty dehydrated. So now you have to hydrate like a crazy-man, eat dinner, and still try and get to bed at a decent hour (assuming you work at least some of the time and/or are doubling). And dehydration causes loss of appetite so eating enough to recover becomes that much harder. But all the same I prefer that to the morning.
2. Run slower and trust that you'll still be fit.* I used to get really upset that the same 9 mile run I was effortlessly cruising in 55 minutes back in April had now turned into a strained 61 minute run. So then I'd try and run harder to prove to myself I was still fit and all that did was train me into the ground.
*When the weather breaks in mid-September (or maybe October for your state) your times will drop without any effort. It always works that way. Just get the work in and trust yourself.
3. I basically had to deal with the fact that every run over 70 minutes was going to be a struggle. Nothing like doing a 2 hour run where your last 50 minutes are 30-45 seconds slower per mile than your first 75. There's really three things you can do about this - 1. Don't do long runs or limit them (not sure how I feel about that). 2. Try harder to get water/carbs on your run. I wish I had hid water bottles when I was younger but I didn't want to seem like a Runner's World type guy. Instead I would just "deathmarch" home on my long runs. Take the extra time to stash water/gatorade whatever on your runs - it helps. Or run with a friend, start at one person's house and run to the other - pound fluids (a hose in the back is gold) - then run back. Try and keep moving though (don't stop for 10 minutes to hit on the dude's sister, drink and go). 3. Instead of sticking to a strict schedule try and pop that long run on the best day for it. For example, if it rains on a Wednesday but you had planned on going long on Saturday (but it's supposed to be 95 and sunny on Saturday) then do your long run on Wednesday. Obviously this isn't ideal and you have to be somewhat intelligent with it (don't run long 2 out of 3 days and then not again for 17 days) but it might save you a little misery.
Good luck.