Every compressor has some sort of cooler. Why? When air is compressed, a lot of heat is generated (read: most of your expensive energy will be converted to heat, only 4% will be compressed air energy).
To get rid of all this heat, your air compressor has 1 or more coolers.
Small air compressors (the reciprocating piston type) have the simplest form of cooler: fins around the discharge pipe (the pipe between your compressor and the receiver/tank).
Bigger air compressors (of the rotary screw type) have normally 1 oil cooler and 1 after cooler. The oil-cooler will cool the hot oil before it is returned to the compressor element.
The after cooler will cool the compressed air before it comes out of the compressor.
Many times, both coolers are mounted next to each other, with one fan to blow cooling air through it.
Testing pressure: 20 bar