In this work, we start with several concerns regarding Galilean variance, pointed out by Christov and Jordan (2005), of the Cattaneo-Vernotte heat conduction in moving media. We then describe a generalized heat transport model in moving media and its underlying theory emanating from the Boltzmann Transport Equation, which achieves the Galilean invariance in all the inertial frameworks. The resulting model recovers heat transport characteristics of different scales with respect to both space (from ballistic to diffusive limits) and time (from finite to infinite heat propagation speeds). (C) 2017 Elsevier Ltd. All rights reserved.