A cooling system for a gas turbine engine comprises a passage capable of receiving cooling air, a compartment radially adjacent thereto and axially aligned therewith, an opening therebetween, a valve within the opening, and a heat exchanger received in the compartment. The valve is moveable between a maximum open position and a minimum open position for increasing or decreasing airflow from the passage into the compartment. At the valve minimum open position, a leakage path is provided between the passage and the compartment, whereby cooling air is capable of passing from the passage to the compartment and toward the heat exchanger at all valve positions. A gas turbine engine is also disclosed.