The invention relates to a device (26) for cooling an annular outer turbine casing (17), the device (26) comprising at least one circumferentially extending tube (27) having an air inlet intended for conveying cooling air, said tube (27) having a radially inner wall provided with cooling air discharge openings and a radially outer wall arranged axially opposite each other, an air inlet manifold (28), the inlet of the tube (27) opening into said manifold (28), characterized in that the tube (27) comprises at least one intermediate wall extending over a circumferential portion of the tube (27) from the air inlet, the intermediate wall being located radially between the radially inner wall and the radially outer wall, the radially inner wall and the intermediate wall forming a first air conveying duct, the radially outer wall and the intermediate wall forming a second air conveying duct extending circumferentially beyond the first air conveying duct, relative to the air inlet.