Definately not. It's the higher temps, above 75 degrees, that you want to worry about. Mice and rats can overheat pretty quickly. Just so you give them things to burrow in and keep warm(toilet paper, cotton balls shredded up, kleenex) they are happy. If you have a screen lid, you can also cover a part of it with a towel so it doesn't get too drafty. That's what we have to do with our nekkid ratties, they get a little cold Hope that helps.