This has been invented many times.
My version first heated the air by extracting heat from the exhaust system, used a turbine to produce power, and finally cooled the air again before it went into the engine.
2010: 454.92L for 5313.90km => 8.56L/100km (27.5MPG US)(5 Months)
2011: 606.11L for 7754.04km => 7.82L/100km (30.1MPG US)
2012: 379.81L for 5940.00km => 6.39L/100km (36.8MPG US)
2013: 348.89L for 5781.00km => 6.04L/100km (39.0MPG US)
2014: 302.29L for 5047.00km => 5.99L/100km (39.3MPG US)
2015: 441.98L for 8024.00km => 5.51L/100km (42.7MPG US)
2016: 128.75L for 1875.00km => 6.87L/100km (34.3MPG US)