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When two electrolyte solutions of different temperature are placed in contact, a thermal diffusion potential (TDP) is established. The phenomenon is studied numerically using finite element simulations of the temperature distribution within a hydrodynamic cell. Experimentally, the hydrovoltaic flow cell is used to demonstrate how a temperature difference can induce redox reactions at electrodes placed in the two liquids in order to extract a current continuously in an external circuit resulting in a power-generating unit. When the concentration of the redox couple introduced in the solution is moderated, it is shown that the TDP is not negligible, even if the main driving force is due to the temperature effect on the standard potential of the couple present. The numerical model may also be applied in more general situations involving thermal effects in microsystems.