Buildings represent a large part in terms of fossil energy consumption, which depends on the great need for heating. Even if the solar absorption heat storage system is possible, the performance of this system is affected by the cycle limits and the climatic conditions. The goal of the present study is to control the thermal performance of the system cycle according to the imposed climatic conditions of Bucharest city, Romania, and therefore a numerical model was developed for this purpose. The scheme and the thermodynamic cycle, the energy and mass balance equations, and the computational algorithm were presented. The results show that the cycle temperature increases at the end of desorption when the heating power supplied to the desorber is increased, which is also proportional to the drop in temperature at the beginning of the desorption. The temperature at the end of absorption and the mass flow rates of the solution have a significant effect on the thermal power released from the absorber and used to heat the building. For an average daily heat power of 1.35 kW/m2 and 10 hours per day of heating the building, the system with a solar colector area of 3 m2 has the capacity of heat supply for all the cold period. However, an economic strategy remains necessary.