A conventional fan does not cool the air itself. It only creates a flow of air that cools the surfaces of other objects.
The ejection fan cools the air already in its housing on 5-10 dergee of Celsius.
This effect is achieved by the fact that the fan cowl has Lavale nozzle-shaped cuts.
When the propeller pump out air from the casing, then air enters through the cone-shaped cuts.
According to Bernoulli's law, air is compressed in a wide part of the cuts, and when it leaves the narrow part, it expands and cools.
The propeller does not spend additional energy on creating a vacuum inside the casing. So the work on cooling is carried out by atmospheric pressure.
Other configurations are possible with different propeller locations: