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Proton exchange membrane fuel cells (PEMFCs) are very promising for both mobile and mid-power stationary applications. Their key component is the solid electrolyte, made with a ionomer membrane with thicknesses in the order of 102 μm, the proton exchange membrane (PEM) that provides proton conduction. This property relies on the hydration state of the membrane, so that water flow and proton conduction are strictly related. As the PEM conductivity relies on a hopping mechanism over barrier energy levels, conductivity is also strongly temperature dependent. This paper presents a highly nonlinear fully coupled dynamic numerical model of the membrane that includes proton conduction, water flow, heat generation and transport and hydration-dependent conductivity. The 3-D model is discretized by means of the finite element method and is used to simulate a typical laboratory PEM. The numerical model is used also for detecting hot spots associated to fluctuations of the PEM thickness.