Parabolic type equations with discontinuous coefficients have long been well studied by many authors. In these papers, the problems are reduced to integral equations by the method of potentials and the well-posedness of various initial-boundary value problems for equations of parabolic type with discontinuous coefficients is proved. In the case without a discontinuity, the spectral theory of these problems is constructed almost completely. In this paper, we substantiate the solution by the method of separation of variables of initial-boundary value problems for the heat equation with a piecewise constant heat conduction coefficient under general non-local conditions and consider some special cases.