An approach to investigation of the thermomechanical processes in solids during cooling under high-temperature annealing and following after annealing thermomechanical conditions is proposed. The annealing is oriented on the relaxation of the residual stresses. This approach is based on the non-stationary thermal conductivity problem, on the problem about a thermoelastoplastic stress and strain state of the thermal sensitive hardenable solids in the deforming process and also on the software based on the finite element method (FEM). As an example the evolution of the residual stress state in disk subjected to annealing and following influence of the static loading applied to the disk hole is analyzed. The hole in disk is coaxial and circular. The residual stresses are specific after coupling by butt welding of two ring disks.