Consult an HVAC contractor first
Closing the heat register and door without sealing the return air duct can actually increase cold air infiltration and cost you more than you thought you’d save.
There are three good reasons to get an HVAC contractor involved before you start closing off heat vents, especially with today’s high-efficiency furnaces and well-balanced systems. First, it might actually add to your heating bill. That’s because with the heat vent closed, the suction from the return air duct can pull in cold air from the outside through any cracks around windows, exterior doors or exterior wall electrical boxes. Second, if the heat duct seams haven’t been sealed properly, the extra pressure from closed-off vents will force hot air through the leaks. That can be as much as 15 percent of heated air into basements, crawl spaces and floor cavities instead of into rooms. Finally, if you have a well-designed, finely tuned heating system, closing off too many rooms can damage your furnace because it has to work too hard to distribute the air. So, if you still want to seal off these rooms, consider hiring an HVAC contractor for advice.