C. acaule seems to handle heat pretty well and even has some tolerance for dry woodlands.
I have first hand knowledge of several scattered populations of C. acaule around the Raleigh NC area, some quite large. Some are in somewhat close proximity to bodies of water, but I've seen them scattered through dry wooded areas and even making gains into people's yards. Raleigh is perhaps slightly higher elevation than Doswell VA from what I'm seeing online, but there's probably not much appreciable difference in the climate, aside from central NC's slightly warmer winters (now considered zone 8a).
I've been told that they're actually a little more common in the sandhills region of North Carolina, which is the eastern part of the state before you get to the coast, than they are here in the piedmont.