Multispindle lathe comprising a machine frame (12), a spindle drum (14) which is arranged in the machine frame (12), is rotatable about a spindle drum axis (16) and is made up at least partially of segments (80) which are cut out from flat material in a stacking direction (82) parallel to the spindle drum axis (16) and extend in stacking planes (88) transverse to the stacking direction (82), these segments having receiving cutouts (90) and cooling channel cutouts (92, 96, 106) which overlap with one another such that the spindle drum (14) has spindle motor receptacles (30) for spindle motors (32) and a cooling channel system (120, 130, 180) separated therefrom by wall webs (98), characterized in that the cooling channel system has several channel subsystems (120, 130, 180) for a liquid cooling medium which are fed in parallel.