The birds could huddle around the tank is the weather was really severe. But, the weight of the tank would become an issue with many existing coops. You can't plop thousand(s) pounds down on a floor designed for a few hundred pounds. So, putting the tank on the ground and pumping the water...
Would it be possible to use a tank full of water or sand as a heat sink? Maybe a 55 gallon drum. The water or sand tank could be heated directly from a solar panel and heating element during the day. The heat would dissipate from the tank into the coop during the night like a hot water bottle...