PURPOSE: To improve operating efficiency while guaranteeing the amount of hot-water securely by a method wherein the operation of an auxiliary heater is controlled by detecting the evaporating temperature of a heat pump and the amount of remaining hot-water.

CONSTITUTION: The setting point of an evaporating temperature detecting sensor 17 is determined to be the point of intersection TEI of a ling L1 showing the heating capacity of the heat pump and the line L2 showing a heat load when the amount of remaining water is zero. In case the evaporating temperature of the heat pump is higher than the set temperature TEI, the operation of the device is effected by only the heat pump. When the evaporating temperature has reduced lower than the set temperature TEI, the switch 17' of the evaporating temperature sensor 17 is closed. In this case, the switch 14' of the remaining hot-water detecting sensor 14 is closed if the amount of remaining water is zero and the auxiliary heater 10 becomes conductive whereby the heating capacity becomes L4 in the diagram and the hot-water temperature is guaranteed. When the amount of remaining hot-water is sufficient, the switch 14' is opened and the hot-water temperature can be guaranteed by using only the high efficiency heat pump without using the auxiliary heater 10 since the heating load L2 is smaller than the heating capacity L1 of the heat pump.