They still need to be able to warm up to 85 or higher to digest their food. If you have a basking spot them no, your house would probably be warm enough. Just make sure the temps in the enclosure are warm enough, don't just go by what the house temp is.
They seem to do better if they cool down at night. Even into the 50's, no worries. (which I doubt your house gets down to, lol)
Make sure you use an accurate thermometer to check your basking temps, and that they are 95-100f under the MVB.