A tool turret for machining workpieces has a housing and with a part that can be rotated around an axis of rotation into several rotary positions. On the rotating part, several tool holders are mounted on the circumference for holding tools to which a cryogenic cooling medium can be fed by means of a first feed line and a respective second feed line. The first feed line can be moved in a linear manner in at least some sections by linear actuator whereby the first feed line is connected in a first position with the second feed line belonging to the tool in work position and in a second position is disconnected from the second feed lines for changing the rotary position of the rotating part. The tool turret enables the cryogenic cooling medium to be fed to the tools in a simple and reliable manner.