Low power adsorption chillers with low desorption temperatures deserve particular attention, because of the possibility of driving them with a solar thermal system integrated with buildings. The monitoring of a recent solar cooling installation in Turin, Italy, has pointed out the opportunity of developing a dynamic mathematical model, in order to simulate the transient performances of this plant. Focusing on the aforementioned low power-low temperature adsorption chiller category, this work proposes a numerical model of the systems, that include a novel zeolite as the adsorbent and water as the refrigerant fluid. The simulation results have been verified by means of the nominal values of one of the very few commercial chillers of this typology available on the market, and have compared with experimental data found in the literature for similar plants.