There are plenty of good reasons to use an intercooler with an engine. Generally, performance cars use intercoolers and there are tons of benefits associated with it. So, let us, first of all, get into the chemistry of it a bit. Hot air is less dense as compared to cold air. That is a simple property of the air. Now, less dense air means, there will be less content of Oxygen in it. This means that the hot air carries fewer Oxygen molecules. The Oxygen molecules in the air are what is actually needed to burn the fuel inside the cylinder of the engine. The more the air (oxygen), the more fuel can be injected into the cylinder and more power could be produced. That is also the reason why Turbochargers are used in modern vehicles.
An intercooler is a heat exchanger used to cool a gas after compression.Often found in turbocharged engines, intercoolers are also used in air compressors, air conditioners, refrigeration and gas turbines.
Intercoolers are used to remove the waste heat from the first stage of two-stage air compressors. Two-stage air compressors are manufactured because of their inherent efficiency. The cooling action of the intercooler is principally responsible for this higher efficiency, bringing it closer to Carnot efficiency. Removing the heat-of-compression from the discharge of the first stage has the effect of densifying the air charge. This, in turn, allows the second stage to produce more work from its fixed compression ratio. Adding an intercooler to the setup requires additional investments.