The behavior of orthotropic layered slabs and cylinders in which the temperature and stress distributions vary in the thickness direction is investigated. A finite element formulation utilizing quadratic layer elements and linear interface elements are used to perform the analyses. The transient heat conduction response is obtained using implicit linear time interpolation including the Crank-Nicolson, Galerkin and Euler backward schemes. It is shown that the modified Crank-Nicolson and modified Galerkin schemes provide computationally economical solutions which are both accurate and free of temporal oscillations. The effects of heat-transfer resistance at layer contact surfaces are illustrated through numerical examples.