With the enhancements in nanotechnology, electronic devices shrank in size which led to a necessity to develop efficient thermal management strategies. These small electronic devices could be thermally managed through passive systems provided that effective materials are developed. Here, we use a layer of activated carbon on top of anodized aluminum heat sinks to utilize the sorption cycle of atmospheric water to create a desorption induced evaporative cooling effect. The material properties of the activated carbon lead to enhanced cooling by radiation and desorption, while the geometry of the heat sinks ensure surface area maximization. We develop a numerical simulation platform to determine the optimum geometry and the optimal activated carbon coating mass. Our results show that as the fin diameter and spacing shrink, and as the activated carbon mass increases within the considered range (0-100 mg), effective cooling of the chip could be achieved. We further employ our simulations to decouple the effects of desorption, radiation, and convection. Our analyses reveal that desorption only plays a vital role during the initial periods of operation, while cooling due to radiation and convection leads to an approximate to 20% increase in the overall steady-state heat transfer coefficient. This study goes beyond introducing a passive thermal management strategy for small electronic chips by providing a link between mass diffusion and thermal processes for effective transient operation of thermal devices.