A heat balancing system for a natural draft gas burning appliance having a flue. When the appliance is in a standby mode, a main burner is shut off and the pilot light remains on. Temperature in the heat exchanger (e.g., temperature of water in a heater tank) may be decreased or increased, respectively, by opening or closing a damper in a flue as needed. If opening the damper does not sufficiently reduce the temperature of the heat exchanger, then the pilot light may be shut off to further reduce the temperature. The pilot light may be turned on again to bring up the temperature. There may be a control or controller to operate the damper to maintain the temperature of the exchanger within a certain range. Electrical power may be provided for the system from a power line, a storage device, or other source.