Abstract: In contrast to reducing the temperature of the heat exchange medium or water so as to conserve on fuel consumption in response to an externally located thermostat or the like upon the occurence of favorable ambient weather conditions, said reduction in accordance with the present invention is, instead, made based on nominal operation of the pump circulating said heat exchange water. The within control that is exercised over the temperature of the heat exchange water to take advantage of mild ambient weather conditions is thus not dependent upon the specific location selected for the thermostat, which location may have more sun and less wind than the spaces or zones being heated. In this and other ways, as hereinafter described, the supervision of the pump provides an accurate and effective control for a hot water heating system that significantly contributes to savings in fuel consumption, but without adversely affecting heating comfort.