A spindle unit comprising a solid shaft main spindle of a highly rigid material such as cemented carbide, with the main spindle being rotatably supported in a spindle head by bearings less apt to generate heat. A tool-clamping device including an adapter attached to a front end of the main spindle, and a tool holder carries a rotary tool. On of the adapter and the holder comprises a short columnar lug, with the other of the adapter and holder comprising a cylindrical hole shrinkage-fitted on the lug. The member having the hole is made of a material having a coefficient of thermal expansion lower than a coefficient of thermal expansion of the other member. The tool-clamping device further comprises heating and cooling devices for heating and cooling the member having the hole.