One-dimensional generalized thermoelastic mathematical model with variable thermal conductivity for heat conduction problem is constructed for a layered thin plate. The basic equations are transformed by Laplace transform and solved by a direct method. The solution was applied to a plate of sandwich structure, which is thermally shocked, and traction free in the outer sides. The inverses of Laplace transforms are obtained numerically. The temperature, the stress and the displacement distributions are represented graphically.