A method for the hourly simulation of air-to-water heat pump systems working in heating mode is developed and implemented through MATLAB. The tool allows to consider both heat pumps with inverter and on–off ones, and takes into account the heat losses from the storage tank. The tool is applied to analyze the seasonal COP of a heat pump system located in Bologna (North-Center Italy), as a function of the bivalent temperature and of the storage volume. The results show that, in the case considered, the optimal value of the bivalent temperature is independent of the storage volume and is lower for heat pumps with inverter. With the optimal bivalent temperature, the highest seasonal COP is obtained without thermal storage.