Thermoelasticity of multilayered cylinders subjected to known temperatures at traction free boundaries are considered. Laplace transform and finite difference methods are used to analyze problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in transform domain. The solution is obtained using the matrix similarity transformation and inverse Laplace transform. We obtained solutions for the temperature and thermal stress distributions in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered composite cylinder with nonhomogeneous materials.