An appliance for heat treatment or inductive heating or cooling of shrink chucks for shaft-type tools or a shrinkage appliance or cooling appliance or shrinkage appliance with a cooling appliance, includes a receiving device or opening receiving a shrink chuck, a heat treatment unit surrounding the receiving device relative to a central axis, an induction coil arrangement or cooling unit, and a measuring unit for temperature measurement of the shrink chuck. For exactly measuring shell temperatures of chucks in receiving openings, the measuring unit has temperature sensors around the receiving device or one temperature sensor inclined around the central axis for contactless detection of the shell temperature, or the measuring unit has sensors around the receiving device including a first temperature sensor for contactless detection of a shell temperature, and a different type of second sensor for detecting another property of the shrink chuck in the receiving device.