Abstract: The invention is a heat conserving space heater that includes a heat source for providing a supply of hot gas of which an example is a gas fired unit heater, air passages in the heater with means for drawing air from the space and exhausting it into the space and when passing through the heater being in heat exchange relationship with the hot gas passages in the heater and an auxiliary heat conserving heat exchanger downstream from the hot gas and air passages and having auxiliary hot gas passages and auxiliary air passages in heat exchange relationship with each other and means in the auxiliary heat exchanger for forcing the hot gas in series through the hot gas passages of the unit heater and through the auxiliary hot gas passages and from there to a place of disposal.