“Intercoolers” cool the air charge from the turbocharger compressor before it enters the engine, but why is this so wonderful? Probably more important than the decrease in air temperature that’s achieved (but that is still useful and important in its own right), is the increase in air charge density that can be achieved by charge cooling.
Air will get hotter when compressed - and hot air is less dense than cool air. So you have a lower mass of air in a certain volume when it’s hot than when it’s cool. The real aim of charge compressing and cooling is to increase the mass of air that is put into the engine’s cylinders.
Remember that air has mass and the number of oxygen molecules available to combust the fuel is directly related to the mass of air in the engine’s cylinders. If we have a fixed volume of air, say 1 Litre, the density of the air is the mass of air contained in that Litre. In the case of air at 15 C and normal atmospheric pressure (about 14.7 psi absolute or about 1.0 bar absolute) the density is 1.225 g/L. As the volume of an engine’s cylinders is fixed, the only way to increase the mass of the air charge in them is to increase it’s density. So first we compress the air. If our turbocharger increases the air to 2.0 Bar absolute (about 30 psi Abs) and the air temperature is still 15 C, the density would be around 2.45 g/L. BUT (and this is the big BUT), if the temperature is greater than our original 15 C the density will be less than 2.45 g/L.
A cooler, denser air charge means we have a greater mass of air available to combust fuel and the more power we ultimately get from our engine. Generally it will also run cooler and be more fuel efficient. So, the answer is to cool the air charge. And the cooler we can get that air, the better.