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Accurate modeling is crucial for the effective design and control of fuel cell stacks. Although physics-based models are widely used, data-driven methods such as the Koopman operator have not been fully explored for fuel cell modeling. In this paper, a Koopman-based approach is utilized to model the thermal dynamics of a 5 kW open cathode proton exchange membrane fuel cell stack. A physics-based model is used as the baseline for comparison. By varying the cooling fan rotational speed, the dynamics of the fuel cell stack were measured from the low load of near 0 kW to about 5 kW. Compared to experimental results, the steady-state absolute errors of Koopman-based models are within 3%. Additionally, once given sufficient dimension, the development effort required for the Koopman-based model is relatively low compared to the traditional physics-based approach, while still achieving a high level of accuracy. These findings suggest the Koopman operator may be a suitable alternative approach for fuel cell stack modeling that enables the development of more accurate and efficient modeling methods for fuel cell systems and facilitates the implementation of the linear optimal algorithms.