Abstract
A solution to the initial-boundary value problem for the heat equation with a discontinuous coefficient and a general conjugation condition is verified using the Fourier method. The problem considered in the paper models the process of heat propagation of a temperature field in a thin rod of finite length, consisting of two sections with different thermal-physical characteristics. In addition to the boundary conditions of the first kind, general conditions are specified at the point of contact of the two media. The existence and uniqueness of a classical solution to the studied problem is proved.