[rotrex]

That "extra" air is provided by your turbo or supercharger. All you do is changing its flow and pressure ratio. As long as your boost is regulated, you will maintain the pressure, but get extra air though a increase in air density. In case of a unregulated supercharger like in my set-up, boost actually drops as you cool more. What makes the power is the charge density. It is determined by both pressure and temperature.