[AXMonster]

For modern cars the old rule of fuel in = power out still applies. The difference that air intake temperature makes is in the variable turbine geometry turbo.

When the engine is running the sensors feed back all the data to the ECU, which calculates the boost requirement based on an air density map. Basically the VGT is set to produce sufficient boost based on the fuel demand and the density of the incoming air. If the air is warm it will need more boost pressure to reach the density to ensure no smoke. Conversely if it is cold it will require a lower pressure.

This has a knock on effect on the pre-turbine exhaust pressure, and in fuel economy terms the amount of work the piston has to do to push the exhaust gasses out of the cylinder and past the exhaust turbine. If the turbine does not need to drive the compressor produce as much boost pressure then the amount of work done on the exhaust stoke is less. So..... lower air intake temperature (post intercooler) = less energy absorbed on the exhaust stroke.