High-temperature proton-exchange membrane fuel cells (HT-PEMFCs) with phosphoric-doped polybenzimidazole (PBI) membranes have a higher operating temperature compared to the PEMFCs operating below 373.15 K. The fuel cell is first heated from room temperature to the minimum operating temperature to avoid the generation of liquid water. The existence of liquid water can result in the loss of phosphoric acid and then affect the cell performance. In this study, the start-up process of HT-PEMFCs is numerically studied by establishing a three-dimensional non-isothermal mathematical model. Preheated gas is supplied into gas flow channels to heat the fuel cell, and then voltage load is applied to accelerate the start-up process. Effects of voltage (0.9 V, 0.7 V and 0.5 V) and flow arrangement (co-flow and counter flow) on temperature, current density, proton conductivity and stress distributions of fuel cells are examined. It is found that the maximum stress is increased when a lower voltage is adopted, and the counter-flow arrangement provides a more uniform stress distribution than that of co-flow arrangement.