Abstract: For cooling and/or heating a machine casing, a method and an arrangement is disclosed in which the machine casing is provided with cooling channels in which pipes are received. Between the pipes and the walls of the cooling channels, a cavity remains through which a cooling medium is circulated. A liquid heat exchange medium is circulated through the pipes. In order to vary the heat energy exchanged per time unit between the pipes and the machine casing, the kind of the medium circulating in the cavities is changed, or its composition is changed, or the flow velocity of the heat exchange medium is varied, or any desired combination of the above measures is realized. Thus, the heat flow, i.e. the exchange of heat energy per time unit, can easily be influenced by the provision of cavities between machine casing and heating or cooling medium by controlling its limiting heat exchange factors, i.e. thermal conductivity and heat transfer resistance.