This device comprises: a compression unit (4) having a plurality of stages, said unit being provided with gas from the cryogenic tank (2) and supplying the gas at a motor supply pressure, a reliquefaction system (20) having an outlet for liquid to the cryogenic tank (2), and an exchanger (10) disposed between the cryogenic tank (2) and the compression unit (4) to heat the evaporation gas from the tank (2) before it enters the compression unit (4). The evaporation gas from the cryogenic tank (2) is heated by gas compressed inside the compression unit (4) to a pressure lower than the motor supply pressure. The reliquefaction system (20) is supplied with gas compressed inside the compression unit (4) to a pressure lower than the motor supply pressure.