A turbine engine is disclosed. The turbine engine may have a first compressor configured to pressurize inlet air, and a second compressor configured to further pressurize the inlet air. The turbine engine may also have a cooling circuit fluidly located to cool the inlet air after the inlet air is pressurized by the first compressor and before the inlet air is further pressurized by the second compressor. The cooling circuit may have a first heat exchanger configured to transfer heat from the inlet air to a fuel of the engine, and a second heat exchanger configured to transfer heat from exhaust of the engine to the fuel of the engine.