The description of heat conduction in microstructured solids is presented in the framework of the dual internal variable approach. One of the internal variables is identified with microtemperature, i.e. the fluctuation of macroscopic temperature due to the inhomogeneity of the body. It is shown that the microstructure influence may result in a hyperbolic heat propagation for the microtemperature. The macroscale heat conduction is described by a parabolic equation which is coupled with the hyperbolic equation for the microtemperature. (C) 2016 Elsevier Ltd. All rights reserved.