Although maintaining polymer electrolyte fuel cells (PEFC) at temperatures below 80 degrees C is desirable for extended durability and enhanced performance, the automotive application also requires the PEFC stacks to operate at elevated temperatures and meet the heat rejection constraint, stated as Q/Delta T < 1.45 kW/degrees C, where Q is the stack heat load for an 80-kW(e) net power PEFC system and Delta T is the difference between the stack coolant temperature and 40 degrees C ambient temperature. We have developed a method to determine the optimum design and operating conditions for an automotive stack subject to this Q/Delta T constraint, and illustrate it by applying it to a state-of-the-art stack with nano-structured thin film ternary catalysts in the membrane electrode assemblies. In the illustrative example, stack coolant temperatures >90 degrees C, stack inlet pressures >2 atm, and cathode stoichiometries <2 are needed to satisfy the Q/Delta T constraint in a cost effective manner. The reference PEFC stack with 0.1 mg/cm(2) Pt loading in the cathode achieves 753 mW cm(-2) power density at the optimum conditions for heat rejection, compared to 964 mW cm(-2) in the laboratory cell at the same cell voltage (663 mV) and pressure (2.5 atm) but lower temperature (85 degrees C), higher cathode stoichiometry (2), and 100% relative humidity. (C) 2016 Elsevier B.V. All rights reserved.