Why does a thermoelectric power generator need both a heat source and a cooler heat sink?

A thermoelectric power generator requires both a heat source and a cooler heat sink to establish a temperature differential ($\Delta T$) across the device's semiconductor legs.12

This temperature gradient is essential because the device operates on the Seebeck effect, which generates an electromotive force—and thus electric power—proportional to the difference in temperature between the hot and cold junctions. Without a heat sink to maintain a lower temperature, the system would reach thermal equilibrium, the temperature differential would vanish, and the generation of electricity would cease.13

Essentially, the heat source provides the energy input, while the heat sink allows for the necessary heat flow through the converter, enabling the direct conversion of thermal energy into direct current. This process is consistent with the fundamental requirement that heat must enter the hot junction and leave the cold junction to perform work.23