controller 62 heat in the tank 31 in accordance with an important aspect of the invention is used to heat the space 19 at appropriate times between periods of operation of the engine 12 and heat pump compressor 11 in a simple effective control strategy the controller 62 for successive periods of heat demand alternates modes of heat supply between 1 operation of the heat pump 11 and 2 exchange of heat from water in the tank 31 without heat pump operation in the latter mode the controller 62 operates the pump 41 to circulate water from the tank 31 to the coil 17 also in this mode the valves 42 45 and 49 are preferably moved by the controller 62 to positions in which the coil 57 is bypassed by water circulating from the tank 31 during operation in the first mode i e heat pump operation heat rejected by the engine 12 depending on the positions of the valves 42 45 and 49 as determined by the controller 62 can be stored in the tank 31 or simultaneously stored in the tank 31 and exchanged at the duct coil the last of these options is performed when these valves 42 45 and 49 are in their illustrated positions this last option may be the preferred mode during the coldest weather when heat demand is high as the temperature of the air delivered to the space will be maximized in the illustrated arrangement all of the rejected heat of the engine 12 is routed.