Abstract: The invention describes a heat-shrink chuck for clamping tools by means of a shrink fit, having a chuck body (1), capable of being secured on the working spindle of a machine tool, in which a central receptacle (2) is configured for the shaft (3) of a tool that is to be clamped, which is characterized in that the central receptacle (2) is configured in noncircular fashion and has along its circumference multiple clamping regions, arranged spaced apart from one another and lying on a common diameter, by way of which the shaft (3) is clamped; and damping regions (5) of greater diameter are configured between the clamping regions (4).