Abstract: The invention relates to a coordinate thermal-cutting machine with a means for automatically setting the initial height of a torch, in particular a plasma torch, above a workpiece surface. In order to achieve a fast and exact setting of the igniting distance above the workpiece surface, the torch (28) is at least partially surrounded by an inner tubular enclosure (7), which is at least partially surrounded by an outer tubular enclosure (10), bearing elements (8, 9 and 29, 30) being arranged between the tubular enclosures (7, 10) in such a way that the inner tubular enclosure (7) is at least longitudinally displaceable with the torch (28), there also being provided a position sensor which senses the longitudinal displacement and, furthermore, the inner enclosure (7) is connected to a compensation device (35) which reduces the weight of the inner enclosure (7) with the torch (28).