This paper presents an efficient and accurate numerical method for estimating transient temperature profile of hot spot in a catalytic packed bed reactor. The method employs an extended Kalman filter and a dynamically adaptive grid technique. Distinct from the conventional fixed grid method, the adaptive grid method dynamically generates grids for calculation based on the state distribution. This technique is a useful tool increasing the accuracy and reducing computational costs for solving partial differential equations. Simulated results for a packed bed reactor showed that the proposed method gives more accurate estimation of the hot spot temperature distribution than the conventional fixed grid based an extended Kalman filter without increasing the computation cost.