A thermo-electrical model of fuel cell proton exchange membrane is developed and the stability of the system is studied. The marginal curves have been obtained as a function of governed dimensionless parameters. The determined dimensionless parameters allow analyzing different scenarios of non-controlled membrane heating. It has been shown that a positive thermo-electrical feedback can cause instability development and membrane damage in real systems. Recommendations for the improvement of heat management in fuel cells have been proposed using the provided stability study. In particular, it has been demonstrated that decreasing of gas diffusion layer thickness has positive effect and stabilizes the system. (C) 2011 Elsevier Ltd. All rights reserved.