Abstract: During the fire-polishing of a lengthwise extended glass body (3), for example a preform for drawing optical fibers, the glass body (3) is held by a holding device (5, 7), and is heated by a burner (23) moving at a variable advancing speed parallel to the lengthwise axis (19). The surface temperature of the glass body (3) is determined with a temperature measuring device (25). The mechanical stress condition of the glass body (3) is detected with an optical device (29) and can be controlled by varying the burner temperature and/or the advancing speed of the burner. The invention makes it possible to counteract the occurrence of high mechanical stresses in the glass body (3).