A cryogenic cooling apparatus comprises a supply gas line and a return gas line adapted to be coupled to a compressor. A coupling element is positioned in gaseous communication with the supply and return gas lines, the coupling element being adapted in use to supply gas to a mechanical refrigerator so that the pressure of said supplied gas is modulated by the coupling element in a cyclical manner. A sensing system is used to monitor the operational state of the mechanical refrigerator and a control system modulates the frequency of the cyclical gas pressure supplied by the coupling element in accordance with the monitored operational state. The mechanical refrigerator has a first cooled stage and a second cooled stage, the second cooled stage being adapted to be coupled thermally with target apparatus to be cooled. A selectively coupleable thermal link is provided for thermally coupling the first cooled stage of the mechanical refrigerator to the second cooled stage in dependence upon the operational state of the mechanical refrigerator. A method of use of the apparatus is also disclosed. The apparatus and method have particular application in a Magnetic Resonance Imaging system.