A turbofan engine including an exhaust casing traversed by a primary flow and surrounded by a secondary flow and an outlet cone carried by this exhaust casing, the exhaust casing and the outlet cone together defining an internal space. The exhaust casing includes a hollow radial arm traversing the primary flow in order to convey part of the secondary flow so as to form a cooling flow for supplying the internal space, and the outlet cone is terminated by an opening for discharging the cooling flow.