Details about a model developed to analyze a complex space heating system are given. Solar air heaters provide thermal energy for driving a vapor compression heat-pump and for other purposes. A (sensible heat) thermal energy storage (TES) unit ensures a more efficient usage of the collected solar energy. The TES operation is described by two non-linear coupled partial differential equations for the temperature of storage medium and heat transfer fluid, respectively. The two main operating modes of the space heating system are presented. The electric power required by the motor of heat-pump's compressor is lower in case of the space heating system that includes a TES unit as compared to the simple solar-assisted heat-pump system. The saving in electric energy varies between 20-35% (during the months when the TES unit is uncharged) and more than 50% (for the months when the TES unit is charged).