A method for cooling a cylindrical workpiece during wire sawing includes applying a liquid coolant to a surface of the workpiece. The workpiece is made of semiconductor material having a surface including two end faces and a lateral face. The method includes sawing the workpiece with a wire saw including a wire web having wire sections arranged in parallel by penetrating the wire sections into the workpiece by an oppositely directed relative movement of the wire sections and the workpiece. Wipers are disposed so as to bear on the surface of the workpiece. The temperature of the workpiece is controlled during the wire sawing using a liquid coolant applied onto the workpiece above the wipers so as to remove the liquid coolant with the wipers bearing on the workpiece surface.