A cooler (10, 110, 210) operating according to the Stirling cycle, comprising: - a housing that defines an internal volume filled with a fluid, the said housing including a compression cylinder and a regeneration cylinder; - a movable compression piston (46, 246) that can move in translational motion in the compression cylinder; - a movable regeneration piston that can move in translational motion in the regeneration cylinder; the housing and the compression piston and the regeneration piston respectively defining a compression chamber, a regeneration chamber, and a reference chamber disposed between the compression piston and the regeneration piston; - a driving crankshaft, comprising a rotating crank pin, that can rotate relative to the housing; and - a compression connecting rod (42, 242) coupled to the compression piston and a regeneration connecting rod coupled to the regeneration piston, the said connecting rods being rigid, with the said connecting rods in addition being coupled to the rotating crank pin; the rotating crank pin and the compression and regeneration connecting rods being disposed in the reference chamber; with the cooler further comprising a fluid flow duct for circulating fluid, a first end (62, 162, 262) of the said duct opening out on to the compression chamber and a second end of the said duct opening out on to the regeneration chamber; the cooler being characterized in that: - the second end of the fluid flow duct is disposed on the regeneration piston; and - the said fluid flow duct comprises a flexible deformable pipe (66, 166) that is deformed in accordance with the movement of the compression piston and/or of the regeneration piston, the said deformable pipe being disposed in the reference chamber; and the first end of the fluid flow duct corresponds to one end of a bore formed in the housing between the compression chamber and the reference chamber, with the deformable pipe extending the said bore. - a housing that defines an internal volume filled with a fluid, the said housing including a compression cylinder and a regeneration cylinder; - a movable compression piston (46, 246) that can move in translational motion in the compression cylinder; - a movable regeneration piston that can move in translational motion in the regeneration cylinder; the housing and the compression piston and the regeneration piston respectively defining a compression chamber, a regeneration chamber, and a reference chamber disposed between the compression piston and the regeneration piston; - a driving crankshaft, comprising a rotating crank pin, that can rotate relative to the housing; and - a compression connecting rod (42, 242) coupled to the compression piston and a regeneration connecting rod coupled to the regeneration piston, the said connecting rods being rigid, with the said connecting rods in addition being coupled to the rotating crank pin; - the second end of the fluid flow duct is disposed on the regeneration piston; and - the said fluid flow duct comprises a flexible deformable pipe (66, 166) that is deformed in accordance with the movement of the compression piston and/or of the regeneration piston, the said deformable pipe being disposed in the reference chamber; and