Hi, I'm in Cedar Grove - which is near Chapel Hill so we basically have the same weather. I guess it depends on how much sunlight hits your coop and run. We put the clear on our run for the reason you mentioned. It's nice in the winter, but during the summer when the afternoon sun hits, it is brutal. We have an open run attached to the enclosed run and that is where the chickens prefer to be during that time. We only covered part of the enclosed run, and are getting ready to cover the rest - DH is going to remove the clear and replace it with the metal roofing panels. Plenty of light will still get in from the sides and it seems to be a bit sturdier than the clear panels. It's also a good idea to have one side higher than the other so the water can easily drain off. I think there is also a semi-clear sort of smokey looking plastic panel that is supposed to block some of the sun rays, but it's pretty pricey. Of course, we have found any time we try to cheap out on something we usually end up having to redo it and so end up spending more than had we done it right the first time.
Good luck!