The classical parabolic model for heat conduction, for many choices of thermal conductivity, predicts an infinite speed of heat diffusion. The hyperbolic model of heat conduction considered here is more physically realistic as a finite speed of heat diffusion is predicted. Exact thermal waves (also called second sound) of this hyperbolic heat conduction model with thermal diffusivity having a power law dependence on temperature are found using the one parameter group similarity method. Both expansive and compressive thermal waves (with discontinuous wavefronts) are graphed and discussed. �� 1993.