Cooling apparatus is provided which comprises a mechanical refrigerator and a heat pipe. 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. The heat pipe has a first part coupled thermally to the first stage of the mechanical refrigerator and a second part coupled thermally to a cooled member which may comprise the second stage of the mechanical refrigerator. The heat pipe is adapted to contain a condensable gaseous coolant when in use. An example coolant is Krypton. The apparatus is operated in a first cooling mode in which the temperature of the cooled member causes the coolant within the second part of the heat pipe to be gaseous and the temperature of the first stage causes the coolant in the first part to condense, whereby the cooled member is cooled by the movement of the condensed liquid from the first part to the second part of the heat pipe. When the cooled member is the second stage of the mechanical refrigerator, the heat pipe provides heat between the higher and lower temperature cooled stages during cooling. An associated method of operating such apparatus is also described.