Abstract: The spindle and the bearings for the spindle in a milling, boring or other machine are cooled by streams of air which is drawn from the surrounding atmosphere by one or more turbine wheels. The turbine wheel or wheels are rotated by the spindle or by a pulley which drives the spindle, and the air streams are caused to withdraw heat from one or more tubes which are adjacent and/or surround the bearings for the spindle. The feature that the turbine wheel or wheels are driven at a speed which is proportional to the RPM of the spindle ensures that the cooling action is also proportional to such speed.