In a nuclear power plant, the thermal energy from the reactor chamber is transported out to the steam generators through a fluid called reactor coolant. Pumps circulating the reactor coolant in a closed loop have a multistage sealing system including a controlled leakage face seal. It is crucial to understand and predict the performance of this mechanical seal to prevent exposure of this radioactive fluid to the environment. This paper introduces a novel modeling approach that allows fast and accurate prediction of the operation of an axisymmetric seal. Thermal and mechanical parameters governing the performance of the seal have been shown to match well with previous experiments. The new model allows investigation of yet unexplored process variables.