A simple and efficient mathematical model for air-breathing proton exchange membrane (PEM) fuel cells has been built. One of the major objectives of this study is to investigate the effects of the Joule and entropic heat sources, which are often neglected, on the performance of air-breathing PEM fuel cells. It is found that the fuel cell performance is significantly over-predicted if one or both of these heat sources is not incorporated into the model. Also, it is found that the performance of the fuel cell is highly sensitive to the state of the water at the thermodynamic equilibrium magnitude as both the entropic heat and the Nernst potential considerably increase if water is assumed to be produced in liquid form rather than in vapour form. Further, the heat of condensation is shown to be small and therefore, under single-phase modelling, has a negligible effect on the performance of the fuel cell. Finally, the favourable ambient conditions depend on the operating cell potential. At intermediate cell potentials, a mild ambient temperature and low humidity are favoured to maintain high membrane conductivity and mitigate water flooding. At low cell potentials, low ambient temperature and high humidity are favoured to prevent membrane dehydration. (C) 2014 Elsevier Ltd. All rights reserved.