The time-dependent convective boundary condition on the inner wall are the essential causes of flow and heat transfer that induce thermal fatigue in pipes with thermal stratification. A three-dimensional transient inverse heat conduction problem (IHCP) was developed in this work for estimating simultaneously the multi-variables of the time-dependent convective boundary condition. Conjugate gradient method (CGM) is chosen as the optimization method. The known parameter in the IHCP is the measuring temperature on the outer wall. Experiments under different seven operating conditions have been taken for the validation of the method. Based on the estimated results, the influence of volume flow rate of cold water on the conductive heat transfer coefficient near the inner wall in the test section and the temperature distribution of the pipe wall were discussed. (C) 2018 Published by Elsevier Ltd.