An x-ray unit has an x-ray radiator having an anode that emits x-rays upon being struck by electrons, a cathode that thermionically emits electrons upon irradiation thereof by a laser beam, electrical connections for application of a high voltage between the anode and the cathode to accelerate the emitted electrons toward the anode as an electron beam, a vacuum housing that can be rotated around an axis, an insulator that is part of the vacuum housing and that separates the cathode from the anode, a drive that rotates the vacuum housing around its axis, an arrangement for cooling components of the x-ray radiator, and an arrangement that directs the laser beam from a stationary source, arranged outside of the vacuum housing, onto a spatially stationary laser focal spot on the cathode and that focuses the laser beam. The x-ray unit furthermore has a control circuit with which an operating property of the x-ray unit is adjusted and at least one measurement element for measurement of a measurement quantity is effectively correlated with the temperature of the cathode. The control circuit adjusts the operating property dependent on the measurement of the measurement quantity.