Heat pump control system and method of operating to provide automatic backup heating modes

A heat pump type heating and air conditioning system includes a gas furnace or other auxiliary heat source and a thermostat and controller associated with the heat pump and the auxiliary heat source for automatically energizing the heat pump if the auxiliary heat source is inoperative regardless of whether or not the automatic heating mode has been selected or the auxiliary heating mode has been selected by the user of the system. A method of operating a heat pump system with an auxiliary heating source to automatically change from operation of the heat pump to the auxiliary heating source depending on conditions such as outdoor temperature, and to automatically change back to operation of the heat pump if the auxiliary heating source is inoperable.