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 space- and time-dependent base heat flux of a cylindrical pin fin from the knowledge of temperature measurements taken within the medium. The inverse solutions have been justified based on the numerical experiments in which three specific cases to determine the unknown base heat flux are examined. The 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 an excellent estimation on the space- and time-dependent base heat flux can be obtained for the test cases considered in this study.