An inverse thermoelasticity problem of identification of inhomogeneous prestressed state of an infinitely long hollow cylinder with a coating is formulated. The characteristics of cylinder's material are described by piecewise continuous functions. A direct thermoelasticity problem is solved on the basis of the shooting method and inversion of solutions based on the Durbin method after applying the Laplace transform. The nonlinear inverse problem is solved by constructing an iterative process, at each stage of which the operator equations of the first kind are solved. The most informative time intervals for gaining the additional information are determined. The influence of prestress level, coupling parameter and coating thickness on the results of prestress reconstruciton is analyzed.