Proton exchange membrane fuel cells are widely used in the automotive and aviation fields due to their high efficiency and environmental friendliness. However, the long starting time of fuel cell vehicles at low temperatures restricts large-scale commercialization. In this work, for the problem of rapid ice melting during a cold start, it is found that when Fourier’s law is adopted, the error is as much as three times higher compared with the non-Fourier heat conduction law, and for ice, the influence of latent heat cannot be ignored, so a novel non-Fourier ice heat conduction model considering latent heat via specific heat capacity functionalization is established. The results demonstrate that the temperature curve first remains unchanged with time and then changes suddenly after the arrival of the heat wave. When the temperature rises to the phase change range, the temperature hardly changes before the completion of the phase change, and then finally rises slowly. Changing the thermal relaxation time may significantly affect the temperature response. The research conclusions of this paper have scientific guiding significance for the materials and structures working in extreme thermal environments such as low temperatures and ultra-high temperature change rates, as well as the design of fuel cell vehicles.