A cryogenic fuel supply system includes a storage tank, a mixing chamber, an auxiliary heating device, a heat exchanger, and flow distribution devices, and a controller. The storage tank stores cryogenic fuel in a liquid state. The mixing chamber receives various flows of cryogenic fuel in a supercritical or gaseous state, the mixing chamber being connected to a combustion chamber to supply the combustion chamber with cryogenic fuel in the supercritical or gaseous state. The auxiliary heating device heats the cryogenic fuel. The heat exchanger assembly includes a cryogenic fuel/oil heat exchanger and a heat exchanger between the cryogenic fuel and the air circulating in a primary duct of the turbine engine. A flow distribution device is upstream of the auxiliary heating device, and one or more flow distribution devices are disposed upstream of the heat exchanger assembly. The controller controls opening and closing of the flow distribution devices.