This paper presents a thermodynamic model for predicting the cooling performance of a single-bed single-stage silica gel/methanol adsorption refrigeration system. Solar heat was collected through flat plate collectors and then stored in a hot water tank. Desorber bed was heated by the hot water from the hot water tank. The temperature of the desorber bed was varied from 65 °C to 85 °C, and its effect on system performance was observed. A numerical model was developed on the basis of mass and energy balance equations, adsorption equilibrium, and kinetic equations (Dubinin–Astakhov equation) for predicting the performance of the adsorption refrigeration system under the said conditions for four major parts (adsorber, desorber, condenser, and evaporator). A programing code was written in FORTRAN for solving these equations under pre-defined material properties, and the simulation result was observed. A refrigeration effect of 577 kJ with a coefficient of performance (COP) of 0.38 could be produced for a maximum bed temperature of 90 °C, which was restricted up to 90 °C because after this temperature, the input increases more than the refrigeration effect, and COP values reduce due to a reduction in desorption mass.