A device for controlling the clearance between the tips of rotary blades and a stationary ring assembly of a gas turbine, the device comprising a circular control box having at least two annular air circulation strips that are spaced apart from each other in the axial direction, each having a plurality of perforations in order to modify the temperature of the stationary ring assembly by discharging air, an annular air feed channel radially spaced from the air circulation strip, at least one air duct for feeding the feed channel with air, and a plurality of hollow distribution spacers connecting the air feed channel to the air circulation strips in order to feed the strips with air while enabling the air that has been discharged against the stationary ring assembly to flow between the feed channel and the circulation strips in order to be evacuated therefrom.