A gas turbine engine comprising: a high pressure compressor section having a high pressure compressor rotor; a low pressure compressor rotor; a high pressure turbine rotor; a low pressure turbine section comprising a low pressure turbine rotor; a hollow shaft, which connects the high pressure compressor rotor to the high pressure turbine rotor; a low pressure shaft located within the interior of the shaft, the low pressure shaft connecting the low pressure compressor rotor to the low pressure turbine rotor; an intershaft space being defined between the low pressure shaft and the hollow shaft; wherein the high pressure compressor rotor comprises a plurality of disks (R1 - R8) connected to the hollow shaft, each of the disks (R1 - R8) having a rim and a web; a plurality of bore cavities located between the disk rims and the outer diameter of the hollow shaft, the bore cavities including at least one forward cavity (24, 26, 28, 30, 32, 34) and at least one aft cavity (36, 38, 40); and a thermal management system comprising: means for delivering a first stream of cooling air to said at least one forward cavity (24, 26, 28, 30, 32, 34) for controlling disk temperature and shaft temperature in said at least one forward cavity (24, 26, 28, 30, 32, 34); means for delivering a second stream of cooling air to said at least one aft cavity (36, 38, 40)for providing disk web cooling in said at least one aft cavity (36, 38, 40); and means for delivering a flow of cooling air into said intershaft space; characterized by further comprising: means for allowing said first stream of cooling air to exit said at least one forward cavity (24, 26, 28, 30, 32, 34) through said hollow shaft into said intershaft space, whereby said first stream of cooling air exiting said at least one forward cavity (24, 26, 28, 30, 32, 34) is mixed with said flow of cooling air flowing through said intershaft space to form a mixed flow; and means for conducting said mixed flow aft to said low pressure turbine section for cooling purposes. a high pressure compressor section having a high pressure compressor rotor; a low pressure compressor rotor; a high pressure turbine rotor; a low pressure turbine section comprising a low pressure turbine rotor; a hollow shaft, which connects the high pressure compressor rotor to the high pressure turbine rotor; a low pressure shaft located within the interior of the shaft, the low pressure shaft connecting the low pressure compressor rotor to the low pressure turbine rotor; an intershaft space being defined between the low pressure shaft and the hollow shaft; wherein the high pressure compressor rotor comprises a plurality of disks (R1 - R8) connected to the hollow shaft, each of the disks (R1 - R8) having a rim and a web; a plurality of bore cavities located between the disk rims and the outer diameter of the hollow shaft, the bore cavities including at least one forward cavity (24, 26, 28, 30, 32, 34) and at least one aft cavity (36, 38, 40); and a thermal management system comprising: means for delivering a first stream of cooling air to said at least one forward cavity (24, 26, 28, 30, 32, 34) for controlling disk temperature and shaft temperature in said at least one forward cavity (24, 26, 28, 30, 32, 34); means for delivering a second stream of cooling air to said at least one aft cavity (36, 38, 40)for providing disk web cooling in said at least one aft cavity (36, 38, 40); and means for delivering a flow of cooling air into said intershaft space; characterized by further comprising: means for allowing said first stream of cooling air to exit said at least one forward cavity (24, 26, 28, 30, 32, 34) through said hollow shaft into said intershaft space, whereby said first stream of cooling air exiting said at least one forward cavity (24, 26, 28, 30, 32, 34) is mixed with said flow of cooling air flowing through said intershaft space to form a mixed flow; and means for conducting said mixed flow aft to said low pressure turbine section for cooling purposes. means for delivering a first stream of cooling air to said at least one forward cavity (24, 26, 28, 30, 32, 34) for controlling disk temperature and shaft temperature in said at least one forward cavity (24, 26, 28, 30, 32, 34); means for delivering a second stream of cooling air to said at least one aft cavity (36, 38, 40)for providing disk web cooling in said at least one aft cavity (36, 38, 40); and means for delivering a flow of cooling air into said intershaft space; characterized by further comprising: means for allowing said first stream of cooling air to exit said at least one forward cavity (24, 26, 28, 30, 32, 34) through said hollow shaft into said intershaft space, whereby said first stream of cooling air exiting said at least one forward cavity (24, 26, 28, 30, 32, 34) is mixed with said flow of cooling air flowing through said intershaft space to form a mixed flow; and means for conducting said mixed flow aft to said low pressure turbine section for cooling purposes. means for allowing said first stream of cooling air to exit said at least one forward cavity (24, 26, 28, 30, 32, 34) through said hollow shaft into said intershaft space, whereby said first stream of cooling air exiting said at least one forward cavity (24, 26, 28, 30, 32, 34) is mixed with said flow of cooling air flowing through said intershaft space to form a mixed flow; and means for conducting said mixed flow aft to said low pressure turbine section for cooling purposes.