Apparatus for compressing cryogenic fluid in at least one compression stage comprising at least one piston and at least one sleeve delimiting at least one compression chamber, a shaft that is able to move in translation along a longitudinal axis (A), the shaft being connected to the piston(s) or sleeve(s) and being able to move with an alternating movement in two opposite directions to ensure phases of compression and intake of fluid into the at least one compression chamber by moving the at least one piston and the at least one sleeve in a relative manner, characterized in that the shaft comprises a portion of reduced cross section in the longitudinal direction (A), said portion of reduced cross section separating two adjacent parts of the shaft, the shaft also comprising at least one linking element made of material that is less thermally conductive than the constituent material of the shaft, in particular a composite material, said at least one linking element having two ends connected respectively to the two adjacent parts of the shaft.