Personally I wouldn't turn the radiator off. It can drop below freezing indoors in this weather. They won't have their winter coat if they're indoor buns. I would ensure that they have a place with warm blankets on the floor.
Can only say that I've got suspended (floor boards) floors throughout & have moved into 1 room with bun, kept at 18C with difficulty, & the rest above freezing. Temporarily blocking the air bricks outside with cardboard, has helped a lot.