As lunar exploration missions advance, the need for safe and sustainable in situ energy systems has become increasingly critical. This study investigates the thermoelectric performance of Bi₂Te₃-based thermoelectric materials under the natural temperature variations on the lunar surface, aiming to illustrate the potential of thermoelectric generation technology in power supply for a crewed moon base. A numerical approach was employed to assess the energy conversion behavior and optimize the geometric design of a thermoelectric module couple consisting of a P-leg and N-leg. The results indicate that Bi₂Te₃-based modules exhibit promising functionality under cryogenic conditions, highlighting their potential as an in situ power source during the long lunar night. Furthermore, geometric optimization was shown to significantly enhance the overall thermoelectric performance. The present study illustrates that TEG technology offers a viable pathway toward reliable energy generation in extreme lunar environments, supporting future mission sustainability.