A timing valve is responsive to certain hydraulic rotor speed input signals so as to schedule increased temperatures of air to a turbine shroud support in accordance with the thermal time constants of the rotor. Clearance between the rotor and the shroud is thereby minimized during both transient and steady-state operating conditions. Temperatures are incrementally increased by selectively combining air from the compressor fifth and ninth stage bleed manifolds. Under certain operating conditions, the timing valve is pre-empted and air is provided at a predetermined temperature level as a function of rotor speed only.