A method of cooling a shroud ring in a turbine section of gas turbine engine includes identifying a series of alternating high temperature regions and lower temperature regions of a circumferential temperature distribution about the inner surface of the shroud ring, and impinging cooling air on to an outer surface of the shroud ring. More cooling air is impinged onto regions which correspond to the high temperature regions on the shroud ring than to regions corresponding to the lower temperature regions of the shroud ring.