A cooling arrangement for a gas turbine engine. The cooling arrangement comprises a discharge channel for air flow from a compressor, a first cooling channel and at least one aperture providing communication between the flow of air through the discharge channel and the first cooling channel. A restrictor device in the aperture regulates the flow of air between the discharge channel and the first cooling channel. The restrictor device deforms to vary air flowing through the aperture in response to a physical condition of the engine. This physical condition of the engine may be that of the temperature of air flowing through the discharge channel, the restrictor device responding to regulate the flow of air based on that temperature. The restrictor device may be a two-way shape memory alloy.