A method and apparatus used to compensate for thermal displacement and to correct a positional error caused by the thermally induced displacement of a spindle positioned in response to a numerical control system. The amount of thermally induced displacement of the spindle, at a predetermined point in time after application of electric power to the machine tool, is stored in a memory. When the spindle is to be positioned in response to numerical control data, the commanded amount of spindle movement is compensated by using the amount of thermally induced displacement stored in the memory, and the spindle is then positioned on the basis of the compensated commanded amount of movement.