Proposed is a multi-part cooled piston (1) for an internal combustion engine, which piston (1) is composed of an upper piston part (2) and a lower piston part (6). The upper piston part (2) forms an inner annular cooling duct (11) with the lower piston part (6), which cooling duct (11) is covered by an upper region (31) of the lower piston part (6). The region (31) is of thin-walled design in such a way that it can be deformed in the manner of a plate spring. Simple and fast assembly of the upper piston part (2) on the lower piston part (6), and a fixed and secure screw connection between the two piston parts, result in that the upper piston part (2) is provided on its underside with a blind bore (26) which is arranged centrally and coaxially with respect to the piston axis (25) and has an internal thread (28), and in that the upper region (31) of the lower piston part (6) has a threaded bolt (29) which is arranged centrally and coaxially with respect to the piston axis (25), points upward and has an external thread (30), with the internal thread (28) matching the external thread (30), such that the upper piston part (2) can be screwed to the lower piston part (6) by means of the blind bore (26) and the threaded bolt.