In this work, a dynamic, 2‐dimensional, non‐isothermal model of a PBI‐based HTPEM fuel cell has been developed. The model consists of a five‐layer geometry with gas channels, gas diffusion layers (GDL) and membrane. The catalyst layers are taken into account as infinitesimal thin reaction layers between GDL and membrane. The overall cell behaviour is simulated considering conservation of mass, momentum, species, charge and energy. The model is focussed on CO poisoning of the anode in steady state as well as in dynamic operation. Therefore, a temperature and time‐dependent approach of adsorption/desorption of CO and H2 on the catalyst sites and the electrochemical reactions of the adsorbed species is applied. The temperature dependency of the fuel cell performance is investigated in a temperature range between 125 and 160 °C at pure hydrogen operation. CO poisoning of the anode is analysed with polarisation curves for different CO concentrations as well as the dynamic response during a CO pulse. The model results are validated by experimental data of in‐house measurements.