  By making use of the potentials of the heat conduction equation the integral
equations are derived which determine the heat kernel for the Laplace operator
$-a^2\Delta$ in the case of compound media. In each of the media the parameter
$a^2$ acquires a certain constant value. At the interface of the media the
conditions are imposed which demand the continuity of the `temperature' and the
`heat flows'. The integration in the equations is spread out only over the
interface of the media. As a result the dimension of the initial problem is
reduced by 1. The perturbation series for the integral equations derived are
nothing else as the multiple scattering expansions for the relevant heat
kernels. Thus a rigorous derivation of these expansions is given. In the one
dimensional case the integral equations at hand are solved explicitly (Abel
equations) and the exact expressions for the regarding heat kernels are
obtained for diverse matching conditions. Derivation of the asymptotic
expansion of the integrated heat kernel for a compound media is considered by
making use of the perturbation series for the integral equations obtained. The
method proposed is also applicable to the configurations when the same medium
is divided, by a smooth compact surface, into internal and external regions, or
when only the region inside (or outside) this surface is considered with
appropriate boundary conditions.
