  The Letter addresses the relationship between hyperbolic equations of heat
conduction and microscopic models of dielectrics. Effects of the non-stationary
heat conduction are investigated in two one-dimensional models with conserved
momentum: Fermi-Pasta-Ulam (FPU) chain and chain of rotators (CR). These models
belong to different universality classes with respect to stationary heat
conduction. Direct numeric simulations reveal in both models a crossover from
oscillatory decay of short-wave perturbations of the temperature field to
smooth diffusive decay of the long-wave perturbations. Such behavior is
inconsistent with parabolic Fourier equation of the heat conduction. The
crossover wavelength decreases with increase of average temperature in both
models. For the FPU model the lowest order hyperbolic Cattaneo-Vernotte
equation for the non-stationary heat conduction is not applicable, since no
unique relaxation time can be determined.
