In a three-stage Gifford-McMahon cycle machine, the third cold store has low-temp. and high-temp. regions (1,23) and a thermal armature (24) is fitted to the outer surface of a cylinder (10) in the region of a seal. An inner cold storage element (25) is coupled to one end of the third driver piston (4). An outer cold storage element (26) is connected to a third cooling stage (20) with a magnet (27). Cold storage elements (1-3) are mfd. of an alloy or cpd. contg. a rare earth metal for enhanced cooling efficiency. The heat produced by compression is less than the theoretical heat content of an isothermal expansion chamber.