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 article it deals with the study of propagation of temperature waves in the wall of the hollow cylinder after a sudden temperature change of the internal environment, fuss-causes upon termination of the movement or circulation of the heated stream. 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 of the penetration depth of the temperature wave according to the considered algorithm, depending on the time since the start of heat exposure and their comparison with the existing data for one-dimensional case are given for the implementation of the identification obtained mathematical model. Calculated radial profiles of relative temperature in the cylinder wall within the temperature waves in dimensionless coordinates and the analytical approximation relations for the description of these profiles are presented. The results are compared with the existing analytical solution for an unlimited array in rectangular coordinates and it is marked that 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 minimum temperature on the inner surface of the heated cylindrical structures that will allow the use of engineering methods to verify compliance with industrial safety requirements.