Knowledge concerning the complicated changes of mass and heat transfer is desired to improve the performance and durability of unitized regenerative fuel cells (URFCs). In this study, a transient, non-isothermal, single-phase, and multi-physics mathematical model for a URFC based on the proton exchange membrane is generated to investigate transient responses in the process of operation mode switching from fuel cell (FC) to electrolysis cell (EC). Various heat generation mechanisms, including Joule heat, reaction heat, and the heat attributed to activation polarizations, have been considered in the transient model coupled with electrochemical reaction and mass transfer in porous electrodes. The polarization curves of the steady-state models are validated by experimental data in the literatures. Numerical results reveal that current density, gas mass fractions, and temperature suddenly change with the sudden change of operating voltage in the mode switching process. The response time of temperature is longer than that of current density and gas mass fractions. In both FC and EC modes, the cell temperature and gradient of gas mass fraction in the oxygen side are larger than that in the hydrogen side. The temperature difference of the entire cell is less than 1.5 K. The highest temperature appears at oxygen-side catalyst layer under the FC mode and at membrane under a more stable EC mode. The cell is exothermic all the time. These dynamic responses and phenomena have important implications for heat analysis and provide proven guidelines for the improvement of URFCs mode switching.