This paper presents the parameter identification of an equivalent circuit-based proton-exchange membrane fuel cell model. This model is represented by two electrical circuits, of which one reproduces the fuel cell's output voltage characteristic and the other its thermal characteristic. The output voltage model includes activation, concentration, and ohmic losses, which describe the static properties, while the double-layer charging effect, which delays in fuel and oxygen supplies, and other effects provide the model's dynamic properties. In addition, a novel thermal model of the studied Ballard's 1.2-kW Nexa fuel cell is proposed. The latter includes the thermal effects of the stack's fan, which significantly improve the model's accuracy. The parameters of both, the electrical and the thermal, equivalent circuits were estimated on the basis of experimental data using an evolution strategy. The resulting parameters were validated by the measurement data obtained from the Nexa module. The comparison indicates a good agreement between the simulation and the experiment. In addition to simulations, the identified model is also suitable for usage in real-time fuel cell emulators. The emulator presented in this paper additionally proves the accuracy of the obtained model and the effectiveness of using an evolution strategy for identification of the fuel cell's parameters.