In critical situations such as floods and earthquakes, the relief forces require a refrigeration for pharmaceuticals and vaccines, which could operate without an electrical energy and the alternative energies, such as solar energy, engine exhaust gases heat, and wind energy. In this paper, a refrigeration cycle has been modeled as an adsorption refrigeration cycle with an activated carbon/methanol as adsorbent/adsorbate pair and two sources of energy—solar energy and engine exhaust gases heat. The solar cycle had a collector with area of 1 m2 and the exhaust gas cycle included a heat exchanger with 100 °C temperature difference between inlet and outlet gases. The temperature profile in adsorbent bed, evaporator, and condenser was obtained from modeling. Moreover, the pressure profile, overall heat transfer coefficient of collector and adsorbent bed, concentration, and the solar radiation were reported. Results represented the coefficient of performance (COP) of 0.55, 0.2, and 0.56 for complete system, solar adsorption refrigeration, and exhaust heat adsorption refrigeration, respectively. In addition, exhaust heat adsorption refrigeration has a value of 2.48 of specific cooling power (SCP). These results bring out a good performance of the proposed model in the climate of Iran.