The transient heat conduction problem in two-layer composite wall is solved analytically using spectral analysis. Eigenvalues and corresponding eigenfunctions of the spectral problem for the temperature distribution in composite walls are analysed using the Rouche Theorem. The number of eigenvalues is obtained and the temperature distribution of this complicated problem is given by a formula with calculated eigenvalues. The analytical solution obtained is in explicit form and provides easy determination of temperature rise in heating and thawing applications of composite materials. Copyright (C) 2001 John Wiley & Sons, Ltd.