I was going to illustrate the breyton cycle, a constant pressure combustion cycle with an otto cycle, a constant volume combustion, but it would have been difficult.
However For the piston engine you will find a 6% mass difference for the same volume of air with ten degrees Celsius difference.
The volume of the engine is more important than for a gas turbine. So you want to trap as much mass of air per stroke.
For stoichometric combustion more air will need more fuel, so you wont have improvement in fuel consumption strictly speaking.
However a more powerful engine that is the same displacement will obviously mean it can scale back performance to equal the power of the engine without the intercooler and have less mechanical losses.
And have an overall improvement in fuel efficiency.
In terms of combustion temperature:
6% more air mass per stroke is not insignificant. And you only lose about 4% of in cylinder temperature right before combustion. And this only results in a 1% difference in the flame temperature after combustion.
So in the grand scheme of creating that high heat and pressure after combustion, you don't get much returns from that higher temperature before combustion. In fact you will find that the cooler air gives higher flame pressures as well.
So it's better to have a 6% increase in air mass, than a 1% increase in overall flame temperature. And you will find your improvements in overall efficiency in that increased power density.
There is probably a 20hp difference with using an intercooler. Is it worth the aero benefit? That's an interesting discussion.