Abstract: This paper deals with a mixed initial-boundary value problem for the one-dimensional heat-flow equation. This problem is closely associated with the distribution of the temperature in a honeycomb sandwich used in the shell construction of vehicle. The boundary conditions are more complicated than the usual ones for the one-dimensional heat-flow equation. Under certain hypotheses, the exact solution of this problem can be obtained by the method of the separation of the variables. This solution may be used to check the accuracy of finite difference approximation.