This paper presents a perfect analytical solution of the hyperbolic asymmetric heat conduction equation and the related thermal displacement equation within a long hollow cylinder (plain strain condition) exposed to a harmonic boundary condition. The material is assumed to be homogeneous and isotropic with temperature-independent thermal properties. The standard method of separation of variables is used for solving the problem with time-independent boundary conditions and the Duhamel integral is used for applying the time-dependency. The results show the wave behavior of Non-Fourier thermal stresses and higher oscillation amplitude in comparison with Fourier one. The developed analytic answer can be applied for modeling cylindrical shell of nuclear rod and can be applied as a benchmark to validate the other numerical solutions.