A three-dimensional multiphysics coupled numerical model for a proton-conducting planar single-rib PCEC was developed using COMSOL Multiphysics to investigate electrochemical and thermal behaviors under different operating conditions. The model integrates electrochemical kinetics, mass transport, momentum conservation, and heat transfer to analyze interactions among flow distribution, polarization heat generation, and temperature evolution within the PEN region and flow channels. Experimental polarization curves were used for validation, and the maximum relative error remained within 2.43%. Parametric analyses were conducted to evaluate the effects of operating temperature, air flow rate, air-to-steam ratio, and flow configuration under co-flow and counter-flow operation. Operating temperature was identified as the dominant factor affecting electrolysis performance. Under 1.5 V operation, current density increased by 163.6% in co-flow configuration and 156.9% in counter-flow configuration when temperature increased from 873K to 973K. Higher operating temperature also increased PEN temperature difference from 50.51 K to 129.90 K in co-flow configuration. Air flow rate and gas ratio showed moderate effects on electrochemical performance, with current-density variations remaining within 10-12%, but strongly affected temperature distribution and heat removal behavior. Increasing air flow rate improved oxygen transport and reduced concentration polarization, whereas higher steam fraction improved heat removal and reduced temperature gradients because of the larger heat capacity of the gas mixture. Flow direction showed limited influence on electrochemical performance, with current-density differences remaining within 5-8% under identical operating conditions. However, counter-flow configuration significantly improved thermal uniformity and reduced PEN temperature difference by 60.5-69.8% compared with co-flow operation under 1.5 V electrolysis conditions.