In this paper, it is performed temporal exergy analysis of an adsorption cooling system in which the durations of desorption and adsorption phases are different. For this purpose, a non-flow exergy function is proposed for substituting the general exergy balance equation. Considering that, temporal irreversibility in adsorption beds, condenser, evaporator, and expansion valve, and also the irreversibility due to external thermal coupling, are calculated. The temporal exergy analysis showed that the maximum rate of irreversibility has occurred in the beginning of precooling and preheating processes. The overall exergy analysis revealed that adsorption beds, thermal coupling, and adsorption cycle components are in charge of 77%, 16% and 7% of total irreversibility, respectively. Moreover, results showed that the intensity of irreversibility in preheating and precooling processes is more than the intensity of irreversibility in adsorption and desorption processes. However, the average per-cycle irreversibility in switching time are less than average per-cycle irreversibility in adsorption and desorption duration. Exergy analysis also showed that increasing heat source temperature will enhance irreversibility in cycle components, and this increase is more sensible in adsorption beds.