Adding a intercooler cools the compressed air, allowing more boost and timing and power per pound of boost, on pump gas. Water-methanol injection is another effective way to cool the air charge, again allowing more boost and timing on pump gas.
Also increases charge density (the charge air is thicker and cooler) making more power because there is more air to combust with fuel.
The cooler the temp of the air going into the motor the less likely it will detonate ping knock.
Detontation must be avoided.
Ideally you want to pick up cool air from the front of the car, compress it in the turbo and then cool it back off (thru a intercooler) before it goes into the engine.
if the inlet air cleaner is picking up hot under hood air you have already lost half the battle. Cool air is better.