I sure wouldn't do that...he'd be better off moving to where the heat is for a couple days, IMO, if (IF?) his cage will not have adequate heat as he's used to.

You talked about room temps, but if his cage heat is on thermostat (?), so what if it runs? That's what it's there for...I wouldn't worry about the CHE drying
out the cage for a couple days either, especially with a humid hide...as long as the UTH + CHE = proper range of temps. for a BP, INSIDE his cage.