A system and method for actively managing blade tip clearances in a turbine engine, particularly under steady state operating conditions such as at base load, involves routing a portion of air from a rotor cooling air circuit to a vane carrier or other stationary support structure surrounding the turbine blades. Because the temperature of the air is less than the temperature of the stationary support structure, the stationary support structure will thermally contract when the air is passed in heat exchanging relation therewith. In one embodiment, the air can be passed through one or more passages extending through at least a portion of the stationary support structure. The contraction of the stationary support structure reduces the blade tip clearance because the blades do not contract. Thus, fluid leakage through the clearances is minimized, which in turn can increase engine performance.