The long-term thermal storage by absorption process studied in this paper is devoted to building heating. A demonstrative prototype that can store 8 kWh of heat and produce a heating power of 1 kW has been designed and built. It has been tested in static and dynamic operating conditions, which are compatible with domestic solar thermal and heating plants. The process operating principle, the prototype design and first experimental results are presented and discussed in this contribution. The charging process has been proved successful. The observed power during the charging phases is satisfactory, according to the process design for a real plant (2–5 kW). Absorption during discharging phase is also verified. Discharging tests show that absorption operates in conditions that could allow house heating as the absorber outlet solution temperature can reach 40 °C. However, some problems related to the absorber design have not allowed observing the heat recovery by the heat transfer fluid as expected. Some avenues are explored prior to a new and more appropriate design and eventually a new operating mode. Various aspects such as the use of a heat and mass transfer enhancement additive and stratification in the solution storage tank have also been addressed.