  We consider unsteady heat transfer in a one-dimensional harmonic crystal
surrounded by a viscous environment and subjected to an external heat supply.
The basic equations for the crystal particles are stated in the form of a
system of stochastic differential equations. We perform a continualization
procedure and derive an infinite set of linear partial differential equations
for covariance variables. An exact analytic solution describing unsteady
ballistic heat transfer in the crystal is obtained. It is shown that the
stationary spatial profile of the kinetic temperature caused by a point source
of heat supply of constant intensity is described by the Macdonald function of
zero order. A comparison with the results obtained in the framework of the
classical heat equation is presented. We expect that the results obtained in
the paper can be verified by experiments with laser excitation of
low-dimensional nanostructures.
