I currently live in North Carolina. I moved here from Arizona where I'd been for 5 years but before that I lived in North and South Carolina for the past 30 years.
I can tell you from personal experience that Arizona in the summer is a LOT more dangerous-hot to ride in the heat than the Southeast BUT! The humidity, as others have stated, can turn this place into a hot sweltering, sweat-dripping swamp and it's miserable being on the road in that. As others have stated, go early morning. Late afternoon is the worst.
Wicking and vented jersey material is a must. The worst for me is sweating down my face into my eyes. Get one of those Halo sweat bands and wear that under your helmet or cycling hat. The rubber insert in that band works like a charm to keep the sweat out of the eyes.