When the pressure of the engine's intake air is increased, such as with a turbocharger, the air temperature also increases. In addition, heat from the hot exhaust gases spinning the turbine will also heat the intake air. The warmer the intake air, the less dense, and the less oxygen available for the combustion event, which reduces volumetric efficiency. Not only does excessive intake-air temperature reduce efficiency, it also leads to engine knock, or detonation, which is destructive to engines.
Turbochargers often make use of an intercooler (also known as a charge air cooler), to cool down the intake air.
Note that intercooler is the proper term for the air cooler between successive stages of boost, whereas Charge Air Cooler is the proper term for the air cooler between the boost stage(s) and the appliance that consumes the boosted air.