A solution to the heat conduction equation for multidimensional composite media, with discontinuities of thermal properties, and having contact resistance at inclusion interfaces is presented. The temperature is expressed as an integral over sources and boundary surfaces in terms of a Green function. The solution is thereby reduced to solving the related eigenfunction problem for the Green function. This solution is also expressed in an alternative form utilizing a technique developed by O¨lcer which promotes faster convergence of the eigenfunction expansion in regions of discontinuities. The solution technique is summarized, and numerical results are presented for one‐dimensional layered slabs, with and without contact resistance specified at layer interfaces.