We proposed a numerical method to investigate the thermo-fluid–structural coupled characteristics of a mechanical seal of a reactor coolant pump (RCP), especially during extended loss of AC power (ELAP) operation. We developed a finite element program for the general Reynolds equation, including the turbulence effect to calculate the pressure, opening force, and leakage rate of fluid lubricant and the two-dimensional energy equation to calculate the temperature distribution of the fluid lubricant. We verified the accuracy of the developed program by comparing the simulated temperature distribution and leakage rate of this study with those of previous research. Heat conduction and elastic deformation due to pressure and temperature changes at the seal structure were analyzed using an ANSYS program. The results showed that temperature more significantly affected the elastic deformation of the seal structure near clearance than pressure both under normal and ELAP operating conditions. High temperature and pressure of the coolant under ELAP operating conditions deform the seal structure, resulting in a much smaller clearance of the fluid film than normal operating condition. However, even with a small clearance under ELAP operation, the leakage rate slightly increases due to the high internal pressure of the coolant. This research will contribute to the development of robust mechanical seals for RCPs by accurately predicting the characteristics of mechanical seals, especially when the RCP is operating under ELAP.