A heat pump system including a heat pump apparatus having a compressor, for supplying fluid heated by the heat pump apparatus to a heating appliance, the heat pump system comprising: an outdoor temperature measuring unit for measuring an outdoor temperature; a supply temperature measuring unit for measuring a temperature of the fluid to be supplied to the heating appliance as a supply temperature; characterized in that the heating appliance carries out heat exchange of the fluid with air by natural convection, and in that the heat pump system comprises a COP memory unit for storing values of a COP (Coefficient Of Performance) of cases in which the outdoor temperature and the supply temperature are respectively changed, wherein the value of COP is associated with the outdoor temperature and the supply temperature, whereby as a general rule the higher the outdoor temperature becomes, the more the value of COP increases, and the higher the supply temperature becomes, the more the value of COP decreases; a restrictive temperature setting unit for setting a temperature A as an upper restrictive temperature which is higher than a preset target temperature and which corresponds to a supply temperature for which the COP stored by the COP memory unit has a predetermined value with respect to the outdoor temperature measured by the outdoor temperature measuring unit, and a control unit comprising a processor and for controlling an operating frequency of the compressor, so that the supply temperature measured by the supply temperature measuring unit should become the target temperature, and for temporarily stopping the compressor when the supply temperature becomes the upper restrictive temperature set by the restrictive temperature setting unit. an outdoor temperature measuring unit for measuring an outdoor temperature; a supply temperature measuring unit for measuring a temperature of the fluid to be supplied to the heating appliance as a supply temperature; characterized in that the heating appliance carries out heat exchange of the fluid with air by natural convection, and in that the heat pump system comprises a COP memory unit for storing values of a COP (Coefficient Of Performance) of cases in which the outdoor temperature and the supply temperature are respectively changed, wherein the value of COP is associated with the outdoor temperature and the supply temperature, whereby as a general rule the higher the outdoor temperature becomes, the more the value of COP increases, and the higher the supply temperature becomes, the more the value of COP decreases; a restrictive temperature setting unit for setting a temperature A as an upper restrictive temperature which is higher than a preset target temperature and which corresponds to a supply temperature for which the COP stored by the COP memory unit has a predetermined value with respect to the outdoor temperature measured by the outdoor temperature measuring unit, and a control unit comprising a processor and for controlling an operating frequency of the compressor, so that the supply temperature measured by the supply temperature measuring unit should become the target temperature, and for temporarily stopping the compressor when the supply temperature becomes the upper restrictive temperature set by the restrictive temperature setting unit.