Thermoelectric generators show great promise to operate self-powered sensors/transmitters provided that the temperature difference across the device is maximized. Here, we use passive nanomaterial-based coatings to increase the generated thermoelectric power at low-to-intermediate temperatures (≈30-60°C). We coat the extended surfaces with a highly sorbent chromium-based metal-organic framework (MOF-Cr-101) to maximize the sorption capacity and emissivity. To achieve the best form of coating, we utilize alternative coating methods including spray coating and high-temperature dip coating to coat the prepared metal-organic framework (MOF) solution uniformly on the base materials to obtain the sorbent heat sinks. To test the performance of our novel sorbent heat sinks, we perform thermal tests at stagnant air inside an environmental chamber set to 25°C and 75% relative humidity. Our preliminary experiments on flat copper plates reveal that a steady-state heat transfer enhancement (1 hour after thermal operation) of ≈50% could be achieved due to desorption of the adsorbed water and the enhanced emissivity. To further increase the contribution of desorption and emission from the surface by increasing the amount of sorbent on the heat sink and the exposed surface area, we consider porous structures and extended surfaces (fins) as the base materials. While porous copper foams of 80% porosity reveals a 80% enhancement in the heat transfer coefficient and a remarkable 140% increase in the obtained thermoelectric power, they lack the enhanced surface area that extended surfaces would present. To utilize the advantages offered by the use of fins, we design the extended surface geometry both through the numerical solution of the 1-D transient heat transfer equation and through finite element analyses. While we obtain the coating thickness as a limiting factor from the 1-D simulations, we find the optimal number of fins from the finite element simulations. We further carry out simultaneous numerical optimization to reach the optimal fin design and coating thickness. Our work not only investigates the thermal dynamics of sorbent heat sink operation on thermoelectric generators but it also introduces a highly effective passive thermal management strategy that could be implemented on various boxed small electronic devices.