In order to cool a process container (1), several cooling elements (5,5',5") are fixed to the outer side of a metal container wall (2) by means of threaded bolts (21) that are welded to the container wall (2) in several places. The clamping pressure of the screw nuts (25) that are screwed on the threaded bolts (21) is sufficient to deform a relatively thin base plate (6) of the cooling elements (5,5',5") including their welded cooling channels (7) so that the cooling elements (5,5',5") are pressed against the outer side of the container wall (2). In order to achieve an additional improvement of heat transmission from the container wall (2) to the cooling elements (5,5',5"), a heat conductive paste preventing insulating air gaps is provided between the base plate (6) and the container wall (2).