Abstract. Method to solve the problem for heat equation for solid with variable cross-section with moving boundary is based on use degenerate hypergeometric function. Solution of problem is a linear combination degenerate hypergeometric function. The main idea of this method is to find coefficients and prove the convergence of series.Consider the surface generated by revolution of a curve r y(z,t) about z - axes. Let us assume that the radial component of the temperature gradient in the solid bounded by above surface is negligible in comparison with the axial component, i.e. the solid can be considered as a bar with a variable cross – section that has only axial component of heat flux.