A passive evaporative cooling heat sink (PECHS) enhances the TEG output capacity. The PECHS has excellent evaporative cooling capability and energy-free water transport characteristics. We established a theoretical model of the PECHS cooled TEG, and investigated the influence of the key parameters on the TEG output capacity. The key parameters include the TEG hot-side temperature (TH = 50–150 °C), ambient relative humidity (RH = 0–100%), ambient temperature (Tamb = 0–40 °C), fin height (Lf = 10–60 mm), fin thickness (tf = 1–3 mm), and fin number (M = 7–17). And this research provides a reliable reference example for the subsequent practical application of utilizing PECHS to enhance the TEG output capacity.