Regulation system intended to ensure the flow rate regulation of a duct in which circulates a hot air stream, the regulation system comprising: - a valve equipped with a shutter intended to be housed in the duct, - an upstream air intake intended to be arranged on the duct upstream of the valve, - a downstream air intake intended to be arranged on the duct downstream of the valve, - a regulator comprising an inlet and an outlet and allowing or preventing the passage of the air based on the pressure at its inlet, and - an actuator actuating the shutter and comprising a first inlet and a second inlet, in which the first inlet is fluidically connected to the outlet of the regulator, the regulation system being characterized in that it comprises a cooling system which comprises: - an outer radiator subjected to an air stream, - a housing comprising a first inlet, a second inlet, a first outlet and a second outlet, a first fluidic path, inside the housing, fluidically connecting the first inlet and the first outlet through the housing, and a second fluidic path, inside the housing, fluidically connecting the second inlet and the second outlet through the housing, the two fluidic paths being separated, - at least one heat pipe (152a-b), each heat pipe (152a-b) comprising a first end in contact with the outer radiator and a second end housed in the housing, - a first upstream duct fluidically connecting the upstream intake to the first inlet of the housing, - a second upstream duct fluidically connecting the first outlet of the housing to the inlet of the regulator, - a first downstream duct fluidically connecting the downstream intake to the second inlet of the housing, and - a second downstream duct fluidically connecting the second outlet of the housing to the second inlet of the actuator. - a valve equipped with a shutter intended to be housed in the duct, - an upstream air intake intended to be arranged on the duct upstream of the valve, - a downstream air intake intended to be arranged on the duct downstream of the valve, - a regulator comprising an inlet and an outlet and allowing or preventing the passage of the air based on the pressure at its inlet, and - an actuator actuating the shutter and comprising a first inlet and a second inlet, in which the first inlet is fluidically connected to the outlet of the regulator, - an outer radiator subjected to an air stream, - a housing comprising a first inlet, a second inlet, a first outlet and a second outlet, a first fluidic path, inside the housing, fluidically connecting the first inlet and the first outlet through the housing, and a second fluidic path, inside the housing, fluidically connecting the second inlet and the second outlet through the housing, the two fluidic paths being separated, - at least one heat pipe (152a-b), each heat pipe (152a-b) comprising a first end in contact with the outer radiator and a second end housed in the housing, - a first upstream duct fluidically connecting the upstream intake to the first inlet of the housing, - a second upstream duct fluidically connecting the first outlet of the housing to the inlet of the regulator, - a first downstream duct fluidically connecting the downstream intake to the second inlet of the housing, and - a second downstream duct fluidically connecting the second outlet of the housing to the second inlet of the actuator.