Just FYI, excerpting from "Care of the Domestic Rabbit," by Dr. Chris Hayhow, current president of ARBA:
"The ideal environmental temperature range for the rabbit is 55 to 70 [degrees] F (13-21 [degrees] C). . . . Rabbits are much more tolerant of lower temperatures than higher ones, and often their activity level will increase during extremely cold weather . . .
I don't think spending time in the finished basement would impose a stress on their temperature regulatory system; they might even like that it was a few degrees cooler than the rest of the house, depending on how much you heat your house. . . .
You did say that this was a finished basement, but you did not indicate what kind of flooring it had. If it is a bare floor, I would really recommend adding some throw rugs so that the rabbits can get enough traction to hop comfortably and enjoyably. . .