Transient response of temperature distributions in a Pressurized Water Reactor (PWR) pressurizer vessel wall for the Inadvertent Auxiliary Spray transient has been analyzed with conservatism accounted for the resulting thermal stresses in the regions of the vessel wall which are wetted by the spray water droplets. In order to determine the forced convective heat transfer coefficient at the inner boundary surface of vessel wall where the droplets impinge on and flow down, the transient temperatures of spray droplets when they reach the inner surface of the vessel wall after travelling from the spray nozzle through the pressurizer interior space occupied with the saturated steam-noncondensable hydrogen gas mixture have been predicted. The transient temperature distributions in the vessel wall have been obtained by using the finite element method, and the typical results have been provided. It has been shown that the results of thermal analysis are consistent with representation of the input transient and have plausible physical meaning.