Thermal-electric conversion is crucial for smart energy control and harvesting, such as thermal sensing and waste heat recovering. So far, researchers are aware of two main ways of direct thermal-electric conversion, Seebeck and pyroelectric effects, each with different working mechanisms, conditions and limitations. Here, we report the concept of Geometric Thermoelectric Pump (GTEP), as the third way of thermal-electric conversion beyond Seebeck and pyroelectric effects. In contrast to Seebeck effect that requires spatial temperature difference, GTEP converts the time-dependent ambient temperature fluctuation into electricity. Moreover, GTEP does not require polar materials but applies to general conducting systems, and thus is also distinct from pyroelectric effect. We demonstrate that GTEP results from the temperature-fluctuation-induced charge redistribution, which has a deep connection to the topological geometric phase in non-Hermitian dynamics, as a consequence of the fundamental nonequilibrium thermodynamic geometry. The findings advance our understanding of geometric phase induced multiple-physics-coupled pump effect and provide new means of thermal-electric energy harvesting.