  We consider heat transfer in an infinite two-dimensional square harmonic
scalar lattice lying in a viscous environment and subjected to a heat source.
The basic equations for the particles of the lattice are stated in the form of
a system of stochastic ordinary differential equations. We perform a
continualization procedure and derive an infinite system of linear partial
differential equations for covariance variables. The most important results of
the paper are the deterministic differential-difference equation describing
non-stationary heat propagation in the lattice and the analytical formula in
the integral form for its steady-state solution describing kinetic temperature
distribution caused by a point heat source of a constant intensity. The
comparison between numerical solution of stochastic equations and obtained
analytical solution demonstrates a very good agreement everywhere except for
the main diagonals of the lattice (with respect to the point source position),
where the analytical solution is singular.
