A gas turbine blade ring is cooled by steam whose temperature, pressure and flow rate are controlled so that a clearance between a moving blade tip and blade ring is maintained appropriately. Steam from a steam turbine bottoming cycle (10) flows into a blade ring cooling passage (8) of a gas turbine (1) via piping (12) for cooling the blade ring. The steam, having cooled the blade ring, is supplied into a transition piece cooling passage (9) of a combustor (3) for cooling the transition piece, and is then recovered into the steam turbine bottoming cycle (10) via piping (14). While the steam cools the blade ring, the temperature, pressure and flow rate of the steam are controlled so that thermal elongation of the blade ring is adjusted and the clearance at the moving blade tip is controlled so as to approach a target value. Thus, the clearance is maintained as small as possible in operation and the gas turbine performance is enhanced.