High temperature stratified flow sometimes caused thermal fatigue cracking in power plants. To prevent fatigue damage by stratified flow, it is important to know temperature distribution history in a pipe. In this study, inverse heat conduction analysis method for an elbow model was developed to estimate the inner surface temperature from the measured outer surface temperature. In the method, the transfer function database inter-relating the inner surface temperature with the outer one was used. For several patterns of the temperature history, the inverse analysis simulations were performed and the accuracy of the estimated inner surface temperature was shown.