A turbine engine assembly including a turbine core and a cryogenic fuel system. The turbine core includes: a compressor section; a combustion section; and a turbine section, which are axially aligned. The a cryogenic fuel system includes: a cryogenic fuel reservoir; a vaporizer heat exchanger; a liquid supply line operably coupling the fuel reservoir to an input of the vaporizer heat exchanger; a gas supply line operably coupling an output of the vaporizer heat exchanger to the combustion section; and a second heat exchanger thermally connecting the liquid supply line and the gas supply line to transfer heat from the gas supply line to the liquid supply line.