  An analytical model of unsteady heat transfer in a one-dimensional harmonic
crystal is presented. A nonlocal temperature is introduced as a generalization
of the kinetic temperature. A closed equation determining unsteady thermal
processes in terms of the nonlocal temperature is derived. For an instantaneous
heat perturbation a time-reversible equation for the kinetic temperature is
derived and solved. The resulting constitutive law for the heat flux in the
considered system is obtained. This law significantly differs from Fourier's
law and it predicts a finite velocity of the heat front and independence of the
heat flux on the crystal length. The analytical results are confirmed by
computer simulations.
