A system for controlling blade clearances within a gas turbine engine includes a rotor disk and a rotor blade coupled to the rotor disk. Additionally, the system includes an outer turbine component positioned outward of the rotor blade such that a clearance is defined between the rotor blade and the outer turbine component. Furthermore, the system includes a heat exchanger configured to receive a flow of cooling air bled from the gas turbine engine and transfer heat from the received flow of the cooling air to a flow of coolant to generate cooled cooling air. Moreover, the system includes a valve configured to control the flow of the coolant to the heat exchanger. In this respect, the cooled cooling air is supplied to at least one of the rotor disk or the rotor blade to adjust the clearance between the rotor blade and the outer turbine component.