An aircraft fluid cooling system has an air heat exchanger passed by this fluid, the air heat exchanger including a structure for introduction of air and an air exhaust. The air heat exchanger is installed in a housing located in a flap guide rail fairing connected to one wing of the aircraft. The structure for introduction of air in the air heat exchanger is connected to an air inlet crossing an outer surface of the flap guide rail fairing and an air exhaust of the air heat exchanger is connected to an air output opening outside the outer surface such that air outside the aircraft passes this air heat exchanger to cool the fluid.