We propose a description of heat conduction in rigid solids in which the classical state space of extended thermodynamics is substituted with another one, spanned by a dynamical semi-empirical temperature and a renormalized flux variable, given by the thermodynamic conjugate of the heat flux and proportional to the heat relaxation time and the dynamical temperature gradient. Propagation of heat pulses in dielectric crystals at low temperatures is analyzed, and the results are compared with those obtained by Lebon et al. (J. Phys.: Condens. Matter, 20 (2008), 025223). We propose a possible experiment in order to check what is the most well-suited definition of temperature in non-equilibrium situations.
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