The cryogenic propulsion module comprises a main cryogenic thruster (10), two attitude-controlling secondary thrusters (21, 22), tanks (31, 32, 33, 34) for feeding cryogenic propellants, a device for intermittently pressurizing the tanks (31, 32, 33, 34), and a device for initiating firing of the main cryogenic thruster (10) in intermittent manner while the tanks (31, 32, 33, 34) are intermittently pressurized. The device for intermittently pressurizing a tank (31, 32, 33, 34) comprises a heat exchange circuit associated with a heat accumulator (61, 62) and a device (71, 72) for putting a predetermined quantity of a propellant into circulation in the heat exchanger circuit. The module also comprises a device for heating the heat accumulator (61, 62) in the periods between two consecutive firings.