In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space- and time-dependent inlet temperature and heat-transfer rate on the external wall of a pipe system using temperature measurements at two different locations. It is assumed that no prior information is available on the functional form of the unknown inlet temperature and heat-transfer rate; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The accuracy of the inverse analysis is examined by using simulated exact and inexact temperature measurements. Results show that an excellent estimation on the space- and time-dependent inlet temperature and heat-transfer rate can be obtained for the test case considered in this study. (C) 2008 Elsevier Ltd. All rights reserved.