We show how to determine the local entropy production rate in the various parts of a polymer electrolyte fuel cell producing liquid water from air and hydrogen. We present and solve five sets of transport equations for the heterogeneous, one-dimensional cell at stationary state, equations that are compatible with the second law of thermodynamics. The simultaneous solution of concentration, temperature, and potential profiles gave information about the local entropy production and the heat and water fluxes out of the system. Results for the entropy production can be used to explain the polarization curve, and we find that diffusion in the backing is less important for the potential than charge transport in the membrane. We demonstrate that all coupling effects as defined in nonequilibrium thermodynamics theory are essential for a correct description of the dissipation of energy and also for the small temperature gradients that were calculated here. The heat flux out of the anode was smaller than the heat flux out of the cathode. The cathode surface temperature increased as the current density increased but was smaller than the anode surface temperature for small current densities. This type of modeling may be important for design of cooling systems for fuel cells. The method is general, however, and can be used to analyze batteries and other fuel cells in a similar manner.