This is tough since you don't know the house yet and don't know how high the heat needs to be in just normal conditions. If it were me, yes, I'd camp out to monitor the situation, maybe others wouldn't. If you opt not to, I'd go check the house at least a couple times a day, in the early am and at night. Take normal precautions, open cabinets to plumbing on exterior walls, dripping taps, flush toilets, make sure windows are locked & exterior doors closed properly, do what you need to do to keep the whole house warm, and go around and check things often.

edit: I'd leave interior doors open between rooms so heat circulates throughout. Once you've lived there a while you'll get a feel if you can close some rooms off or not.

I have a walk out basement. Furnace is in the back, the basement stays pretty level. Frostline is probably 12 - 18" below ground so basements are usually okay.