Melissa, Isn't it so frustrating to work with tweaking your MDI when the pump is right around the corner for you! I found that... then again I'd been going at it for a while longer I suppose. I admire you rolling up your sleeves (although it's hardly an option most of the time, is it?).
if I was going low in the morning from a good BG last thing at night, I would suspect my dose is still too high, then I would take some tests through the night to confirm my suspicion. Speaking personally I would be happy to reduce my dose my a small increment again. But I'm not offering that as medical advice - what I would advise is calling or facing your doctor to ask for some guidance.
I was just reading in Pumping Insulin (great book to have going onto the pump.... I'm glad I finally got it) where Walsh states that heat increases the speed of insulin... I find conversely it can make it very sluggish for me, but I think I am pretty weird. It's probably only experimenting and observing that will answer the question if it's the heat having any effect.