Summary: A dynamical thermoelastic problem for a long two-layered cylinder with the internal layer made of an isotropic material and the external layer made of a cylindrically anisotropic material is considered. Using the finite integral transformation, the solution is represented by series of eigenfunctions of the corresponding Sturm-Liouville problem. The asymptotic representations of eigenvalues are given, and the case of a sudden temperature rise is studied.