Recent studies of shock propagation in a one‐dimensional discrete crystal lattice are extended to include the case for which the lattice is at a nonzero intitial temperature. The lattice is assumed to be monatomic, and its atoms are assumed to interact via a Morse‐type interatomic potential. Behind the shock front, a spectrum of well‐defined stable pulses (solitons) is observed to propagate amid the thermal background of the lattice. The solitons have varying amplitude and propagation velocities, and the different velocities introduce a spreading effect which prevents the shock profile from approaching a steady state. The velocity distribution function of atoms well behind the front is calculated and indicates an approach to thermal equilibrium at an elevated temperature in this region of the crystal. The implications of the nonsteady behavior and the slow approach to thermal equilibrium for currently used theories of detonation are noted and discussed.