A gas turbine engine has a row of circumferentially spaced rotor blades and a plurality of seal segments circumscribing the rotor blade tips and attached to a radially inward side of a casing of the engine. The seal segments are spaced from the casing by a spacing cavity. A flow of relatively hot cooling air is routed to the spacing cavity to cool the seal segments. The engine has an external cooling arrangement for impinging relatively cold cooling air on a radially outward side of the casing. The engine has a wall containing a plurality of through-holes which is attached to a radially inward side of the casing adjacent the seal segments. The wall is spaced from the casing to define a heating control chamber between the wall and the casing. The engine has one or more closable ducts which allow air to be exhausted from the heating control chamber.