safe room heaters

This time of year, I see a lot of ads for various types of gas home heaters. They all promise that you'll save money by using them rather than whatever other type of heat you have in your home. Some of them have famous—or formerly famous—people promoting them. Sometimes it's people who look like members of a small religious safe room heaters sect hawking these devices，But are they correct when they say you'll save money by buying and using these small space heaters?