Aircraft propulsion unit with a cooler installed at engine nacelle

The propulsion unit has an air vein (13) guiding pressurized air towards an air pipe (20) arranged between an outer wall (6) and an inner wall (60) of a nacelle (10). A cooler (45) has a parallelepiped volumetric cooling unit (14) i.e. blade, positioned in the air pipe. The cooler has a surface cooling unit (15) i.e. fin, that is not convex towards the volumetric cooling unit. The surface cooling unit is arranged at an outer wall of a connecting strut of an aircraft. The air pipe has an air inlet (21) that is arranged at the front of the nacelle.