Turbomachine component with cooling arrangement

A tube (2) with a minimum internal diameter of 4 mm is secured to the turbine part (1) in order to act as a cooling channel. The tube is secured to the turbine part by welding, soldering or adhesive and includes flexible sections or at least one bellows section (7), has a helical or spiral shape or contains one or more sections connected to each other or to the turbine part via a sliding joint (8) in order to compensate for deformation of the turbine part.