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I don't know where you live or how cold your winters really are so I am at an bit of a disadvantge in discussing this considering your specific cionditions, but the vast majority of people on this forum have no reason to heat their coop. They usually risk doing more harm than good. Heat is usually more harmful to chickens than cold. Chickens wear a down coat to keep them warm. Try putting on a heavy down coat and then sit in a heated room. That can get pretty uncomfortable pretty fast.
As long as they are protected from direct breezes hitting them and they have adequate ventilation, you'd have to live where it is extremely cold, like a long way below zero Fahrenheit, for cold to be a concern. The big danger is frostbite, not them freezing to death. If you have high humidity in the coop, they can get frostbite at temperatures just below freezing. But with decent ventilation, preferably openings higher than the birds when they are roosting, they can easily survive 20 below zero Farenheit or even colder.
It helps a lot if they are allowed to acclimatize. If you pump warm air into them and then the power goes out, they could be in serious trouble. A dryer would be pumping moist air in the coop when it is drying clothing. Not good. Do you plan to run the dryer full time? If not those temperature swings would not be good for them, even if the power never goes out.
What do I think? BAD idea, but I am glad you asked. It's better to ask than hurt your chickens. And once again,
