Wow. Mice in a totally dark room. They'll forever be perpetually having sex. OR die early. Has anyone seen the movie "People Under the stairs"? If we keep our mice like that, they'll die early, may not produce mice. My parents tried this on a 1:1 colony when I was younger. Its not natural for them. (well maybe the Field and deer mice up here yes because we get some pretty short days.) But from knowing from experience. Its better to keep them in some light thats on a schedule. Its basically for their health and their mind. I know I put my rats in my closet once because a friend came over and they went completely nuts. (I'm not doing that again)
But if you wish to try it out, go for it. As for a room with a water heater. How hot does it get in there. Because,to much heat and mice won't produce. Or if they do. It'll be smaller litters. I mainly say this because mice breed at night, and at night there are cooler temperatures. And if their in a room thats hot 24/7 they might not breed. With snake breeding we try to simulate spring. With mice we try to simulate a perfect night time cool situation. So if that room gets pretty warm. I'd say nix that idea and put them in a cooler room.
Just my .02