The paper presents a method combining the processes of straightening and thermal treatment. Technological processes with axial strain were considered, for the case of heated material and without its heating. The essence of the process in the case of heated material consisted in the fact that if under tension all longitudinal forces in the first approximation are uniform - the same strains are generated. The presented technological approach, aimed at reducing the curvature of axial-symmetrical parts, is acceptable as the process of rough, preliminary machining, in the case of shafts with the ratio L/D≤100 (L – shaft length, d – shaft diameter) and without a tendency of strengthening. To improve the accuracy and stability of geometric form of low-rigidity parts, a method was developed that combines the processes of straightening and heat treatment. The method consists in that axial strain – tension, is applied to the shaft during heating, and during cooling the product is fixed in a fixture, the cooling rate of the shaft being several-fold greater than that of the fixture. A device is presented for the realisation of the method of controlling the process of plastic deformation of low-rigidity shafts. In the case of the presented device and the adopted calculation scheme, a method was developed that permits the determination of the length of shaft section and of the time of its cooling.