In a gas turbine for aeronautic engines, a stator body delimited by an outer lateral surface is cooled by an air cooling device having a plurality of circumferential tubes for distributing air on the outer lateral surface; each circumferential tube having a plurality of outlets for guiding respective cooling airflows towards the outer lateral surface and into a respective circumferential channel obtained between two groups of circumferential channels adjacent to each other and lapped by the flow of air leaving the circumferential channel.