A cooling system for a component of a gas turbine engine, comprising: the component to be cooled; a first airflow passage configured to direct a first airflow to a mixing chamber; a second airflow passage configured to direct a second airflow to the mixing chamber, the second airflow having a higher temperature than the first airflow; and a cooling airflow passage to direct a cooling airflow from the mixing chamber to the component, the cooling airflow comprising the first airflow and the second airflow; characterized in that: the first airflow passage, the second airflow passage, and the cooling airflow passage are configured and sized to allow an amount of cooling airflow for unrestricted engine operation within its normal parameters and operating envelope; and wherein when the first airflow passage is disabled, the second airflow passage and cooling airflow passage are configured and sized to allow an amount of cooling airflow which is adequate to permit continued safe engine operation restricted to within only a portion of its normal parameters and operating envelope; wherein the disabling of the first airflow passage is a control feature, whereby the continued safe engine operation with lesser cooling airflow is an improvement in engine efficiency; wherein the component is a turbine rotor of the gas turbine engine; and wherein a second airflow inlet to the mixing chamber and a cooling passage outlet are configured to prevent backflow of hot combustion gases into the turbine rotor. a first airflow passage configured to direct a first airflow to a mixing chamber; a second airflow passage configured to direct a second airflow to the mixing chamber, the second airflow having a higher temperature than the first airflow; and a cooling airflow passage to direct a cooling airflow from the mixing chamber to the component, the cooling airflow comprising the first airflow and the second airflow; characterized in that: the first airflow passage, the second airflow passage, and the cooling airflow passage are configured and sized to allow an amount of cooling airflow for unrestricted engine operation within its normal parameters and operating envelope; and wherein when the first airflow passage is disabled, the second airflow passage and cooling airflow passage are configured and sized to allow an amount of cooling airflow which is adequate to permit continued safe engine operation restricted to within only a portion of its normal parameters and operating envelope; wherein the disabling of the first airflow passage is a control feature, whereby the continued safe engine operation with lesser cooling airflow is an improvement in engine efficiency; wherein the component is a turbine rotor of the gas turbine engine; and wherein a second airflow inlet to the mixing chamber and a cooling passage outlet are configured to prevent backflow of hot combustion gases into the turbine rotor. the first airflow passage, the second airflow passage, and the cooling airflow passage are configured and sized to allow an amount of cooling airflow for unrestricted engine operation within its normal parameters and operating envelope; and wherein when the first airflow passage is disabled, the second airflow passage and cooling airflow passage are configured and sized to allow an amount of cooling airflow which is adequate to permit continued safe engine operation restricted to within only a portion of its normal parameters and operating envelope; wherein the disabling of the first airflow passage is a control feature, whereby the continued safe engine operation with lesser cooling airflow is an improvement in engine efficiency; wherein the component is a turbine rotor of the gas turbine engine; and wherein a second airflow inlet to the mixing chamber and a cooling passage outlet are configured to prevent backflow of hot combustion gases into the turbine rotor.