Abstract: The invention indicates a device and a process for clamping tools in a clamping chuck which possesses a shrinkage segment (14) to receive the tool, with a heating apparatus (26), preferably designed as a gas burner, being associated with the shrinkage segment (14). The tool is clamped in the clamping chuck (20) with a press fit in the shrinkage seat, resulting in especially high clamping force. To prevent local overheating of the clamping chuck (20) and achieve complete insertion of the tool shaft into the thermally expanded shrinkage segment (14) of the clamping chuck (20), a receiving apparatus (40)--by means of which, for clamping purposes, the tool can be elastically pressed in the axial direction against the shrinkage segment (14)--is provided to receive the tool.