In a method and a machine tool for machining metallic workpieces, a cooling device is provided to supply a cryogenic coolant to a first tool and a precooling device is provided to supply the cryogenic coolant to a second tool. The first tool is held in a first chuck and processes a workpiece, with the first tool during processing being cooled via the cryogenic coolant. The second tool is held in a second chuck and will subsequently be used for processing the workpiece. The second tool is supplied via the precooling device with the cryogenic coolant and thus cooled to the operating temperature required for processing. Due to the fact that the second tool is precooled to the required processing temperature, after the change of tools, the processing of the workpiece can be continued immediately. By precooling the second tool during the primary processing time, the total processing time of the workpiece is reduced, providing the machine tool with higher productivity.