This paper adopts a novel dimensionless investigation of a two-bed adsorption cooling/desalination system. In this regard, various independent dimensionless parameters are introduced. This study carries out parametric and normalized sensitivity analyses to explore the independent dimensionless parameters that significantly affect the cooling/desalination performance of the system. The coefficient of performance is used to assess the system’s cooling performance. On the other hand, a new performance index for water production is adopted. It is defined as the energy coefficient of adsorption desalination. It is observed that the system performance is more sensitive to the variation of the multiplier constant of the adsorption kinetics equation than the variation of the power constant of the adsorption isotherm equation. As the latent-to-isosteric heat ratio increases from 0.5 to 1, a performance enhancement of about 85% takes place. A significant influence is found for a parameter called the dimensionless heat capacity of the adsorption bed. As it increases from 0.2 to 2, a considerable drop of about 40% is noticed in both the coefficient of performance and the energy coefficient of adsorption desalination. A noticeable enhancement in the system performance is recorded as the dimensionless heat capacity rate of the heating fluid increases.