In the use of a distributor or diffuser in the form of a thin-walled, completely or partially air-permeable, heat-reactive layer for drilling or milling machining of a workpiece with a tool, a vacuum, surface tension is produced, which is large enough to fix the position of the workpiece, by using a vacuum over the layer acting as a distributor or a diffuser on the surface of the workpiece to be machined. The workpiece is then machined, and a cutting speed and rate of feed is adjusted, such that a defined local heating takes place in a contact area between the tool and workpiece. The peak temperature at the contact area is greater or the same as a melting temperature of the surface of the distributor or diffuser.