A method and a device for the precision turning of a workpiece made of a heat-treatable steel permits a dry hard precision turning of hardened workpiece surfaces without tempering. In order also to allow precision turning and hardening of unhardened workpiece surfaces which are simultaneous in terms of production time, use is made of the local temporary heating of the workpiece caused by machining. The workpiece surface is heated further locally by the action of a laser beam, in the region directly behind the cutter, up to the transformation temperature of the material to be machined via an optical fiber integrated in the tool. The surface is then self-quenched and, as a result, hardened close to the surface. At the same time, the surface temperature at the point of action of the laser beam can be recorded thermographically and, this actual temperature signal can be used to adjust the power of the laser beam so as to maintain the desired temperature.