A hollow cylinder with thick walls is one of the most complex objects to calculate the unsteady temperature field, so this field is the least studied. However, such objects are found in many modern constructions of systems of generation and distribution of heat. In the proposed work it deals with the study of propagation of temperature waves in the wall of the hollow cylinder with harmonic temperature change of external environment arising from its diurnal fluctuations. The approximate analytical solution is presented by separation of variables in the complex domain with the use of cylindrical functions. The algorithm of calculation of temperature fields numerically is shown using an explicit finite-difference scheme of high accuracy in conditions of cylindrical symmetry with boundary conditions of the first kind. The results of calculations according to the considered algorithm, depending on the time since the start of heat exposure and their comparison with the analytic solution are given for its implementation. Calculated radial profiles of the temperature in the cylindrical wall within the temperature waves and the analytical approximation relations for the description of its damping coefficient are presented. The results are compared with the existing analytical solution in rectangular coordinates and it is marked that they have some differences but the common results are found regardless of the material and geometry of the cylinder, as well as of temperatures of inner and outer environment. Presented dependences are invited to apply for the analytical evaluation of the temperature amplitude on the inner surface of the heated cylindrical structures that will allow the use of engineering methods to verify compliance with industrial safety requirements.