The relativistic heat conduction (RHCE) model is particularly important in the analysis of processes involving moving heat sources (MHS) at speeds or frequencies comparable with those of heat propagation in the medium. This paper establishes a unified framework for solving heat conduction problems using the RHCE model. It offers '' Fundamental Solutions '' in one, two, and three spatial dimensions, for the transient response due to an instantaneous point MHS. Moreover, it presents the transient response due to a continuous point MHS, the quasi-steady response due a periodic point MHS, as well as guidelines for solving the RHCE equation under various loading and boundary conditions. (c) 2005 Published by Elsevier Ltd.