In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to solve the inverse hyperbolic heat conduction problem in estimating the unknown time-dependent inner-wall heat flux of a hollow cylinder from the knowledge of temperature measurements taken within the medium. The inverse solutions have been justified through the numerical experiments in two specific cases to determine the unknown heat flux. Temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors upon the precision of the estimated results is also investigated. Results show that excellent estimation on the time-dependent heat flux can be obtained for the test cases considered in this study. Once heat flux variation is accurately estimated, the evolution of temperature, displacement, and stress distributions can be calculated in great precision. (C) 2013 Elsevier Ltd. All rights reserved.