Linear as well as non-linear contributions to the Zeebeck and Peltier coefficients of a metallic film in contact with the equilibrium metal are calculated within a simple model. The non-linear part of the thermoelectric response survives down to a very low temperature which in principle permits thermoelectric cooling at these conditions. Thermal equilibrium in a metallic constriction between dissimilar metals is evaluated in the non-linear current-carrying regime.