In the work, the temperature stress field is given in a circular disk with variable thickness. If the yield stress limit is exceeded, according to Tresca's criterion, the initial and final pressure on the inner surface, which is necessary for plasticization with a constant temperature distribution, is determined. In addition, the work also deals with the example without superficial loading, when the additional temperature increase causes the material to flow. In this case, the reduction in strength must also be taken into account for full plasticization.