The air stream cooling belongs to the outer cooling, making sure the heat of all critical parts of the engine is immediately handed over to the air.
Parts apt to heat, are designed with large surfaces (cooling fins). Air, is often passed along these surfaces with great speed, often through special channels and/or air buffles. This is done either by the air stream (left) or by a special blower (right).
The engine becomes warm more quickly. If the engine is mounted in the car middle or rear, there are no long coolant ways. A cooling system can neither freeze nor even leak.
The engine is felt to be more noisy than with liquid cooling due to cooling fins and perhaps with blower. Cooling and heating are more irregular. Air absorbs less heat after all and also the heat transfer is more difficult.
Partly still in motorcycles.