In the cooling process, the vessels receiving the hot filling material, which vessels are impinged externally by cooling medium, are continuously turned about at least one axis so that a continuous circulation and mixing of the filling material takes place. The vessels are designed in the manner of barrels having a cylindrical vessel casing and have mixing baffles extending from the walls towards the interior, which mixing baffles convey a continuous circulation and mixing of the filling material on rotating the vessels roughly about their longitudinal axis. The cooling device is an immersion bath filled with a coolant liquid, in which a rotary drive for turning the immersed vessels about their longitudinal axes is provided.
