In the process of cylindrical grinding of parts, a significant amount of heat is released, which has several negative factors affecting the machining process, including reducing the quality of the surface layer of the workpiece, the appearance of burns and cracks; lowering the accuracy of machined parts; instability of the thermal regime of the process. The main consequence of thermal effects is a deformation of the technological system and a decrease in machining accuracy. In this paper, a study of the complex stress state of a cylindrical grinding machine headstock was performed using the finite element method by creating a 3D model of the headstock in the CREO Parametric software and simulating it in the CREO Simulate application. As a result, the values of the edge displacements of the cylindrical surface of the grinding wheel due to the displacement of the spindle axis under the action of force and thermal deformations in the elements of the grinding headstock were established, including their dynamic change during 6 h of machine operation. To compensate for the specified errors, it is recommended to use a coolant supply device developed by the authors, which protects the front wall of the grinding headstock from the ingress of heated coolant and reduces the power of the thermal field on it.