  We study transient thermal processes in infinite harmonic crystals with
complex (polyatomic) lattice. Initially particles have zero displacements and
random velocities such that distribution of temperature is spatially uniform.
Initial kinetic and potential energies are different and therefore the system
is far from thermal equilibrium. Time evolution of kinetic temperatures,
corresponding to different degrees of freedom of the unit cell, is
investigated. It is shown that the temperatures oscillate in time and tend to
generally different equilibrium values. The oscillations are caused by two
physical processes: equilibration of kinetic and potential energies and
redistribution of temperature among degrees of freedom of the unit cell. An
exact formula describing these oscillations is obtained. At large times, a
crystal approaches thermal equilibrium, i.e. a state in which the temperatures
are constant in time. A relation between equilibrium values of the temperatures
and initial conditions is derived. This relation is refereed to as the
non-equipartition theorem. For illustration, transient thermal processes in a
diatomic chain and graphene lattice are considered. Analytical results are
supported by numerical solution of lattice dynamics equations.
  ${\bf Keywords}$: thermal equilibrium; stationary state; approach to
equilibrium; polyatomic lattice; complex lattice; kinetic temperature; harmonic
crystal; transient processes; equipartition theorem; temperature matrix.
