RE: Boost air temp?
Heated air entered in the engine has a disadvantages, heated air means less oxygen who make less power in the engine. The turbocharged engines has intercooler to keep air cooled before entering in the engine.
In some modern cars with common rail dieselengine has electronic controlled air temperature who are about 20 degree celsius, it has both heated air and cooled air from intercooler to regulate constant air temperature at 20 degree.