  We obtained a new representation of a solution of the heat conduction
equation with boundary condition of the third kind for a layer. The result is
presented as a superposition of fundamental solutions for an unbounded system
with variable coefficients, the explicit form of which is given. We consider
the well-known problem of the evolution of the temperature field initially
uniformly distributed in a layer. The distribution of the temperature field is
represented in terms of the obtained functions.
