A gas turbine comprising in series along a main hot gas direction: - a compressor section provided with a plurality of compressor blades and vanes for compressing air; - a combustion section for realizing a mixture of the compressed air and a fuel and for burning the mixture; - a turbine section provided with a plurality of turbine blades and vanes for expanding the burnt mixture; the gas turbine comprising a rotor having a rotor axis and extending from the compressor section to the turbine section for supporting the compressor and the turbine blades; the rotor being made of a plurality of rotor disks (14; 15; 16) adjacently arranged along the rotor axis and shaped for realizing cavities (23, 39) between the respectively adjacent rotor disks (14; 15; 16); the rotor comprising a last rotor disk having a downstream portion for being supported by a bearing and a bearing cover and an upstream portion for supporting a last turbine blade; the rotor further comprising a second last rotor disk for supporting a second last turbine blade; the gas turbine being provided with a cooling duct system configured for supplying cooling air from a downstream end of the turbine section to the last turbine blade and the second last turbine blade passing inside the last rotor disk and the second last rotor disk; wherein the cooling duct system comprises: - an axial bore in the downstream portion of the last rotor disk aligned with the rotor axis; characterised in that the cooling duct system further comprises - a first plurality of inclined radial bores in the upstream portion of the last rotor disk; wherein the first plurality of inclined radial bores in the upstream portion of the last rotor disk is extending from the axial bore to a last radial cavity arranged under a last heat shield arranged upstream of the last turbine blade and wherein the first plurality of inclined radial bores is fluidly connected to a root portion of the last turbine blade through the last heat shield; - a second plurality of inclined radial bores in a second last rotor disk extending from the last radial cavity to a root portion of the second last turbine blade which is in turn fluidly connected to a root portion of the last turbine blade through the last heat shield; - a third plurality of inclined radial bores in the last rotor disk for directly supplying cooling air coming from a bore realized inside the bearing cover to the last heat shield. - a compressor section provided with a plurality of compressor blades and vanes for compressing air; - a combustion section for realizing a mixture of the compressed air and a fuel and for burning the mixture; - a turbine section provided with a plurality of turbine blades and vanes for expanding the burnt mixture; - an axial bore in the downstream portion of the last rotor disk aligned with the rotor axis; characterised in that the cooling duct system further comprises - a first plurality of inclined radial bores in the upstream portion of the last rotor disk; wherein the first plurality of inclined radial bores in the upstream portion of the last rotor disk is extending from the axial bore to a last radial cavity arranged under a last heat shield arranged upstream of the last turbine blade and wherein the first plurality of inclined radial bores is fluidly connected to a root portion of the last turbine blade through the last heat shield; - a second plurality of inclined radial bores in a second last rotor disk extending from the last radial cavity to a root portion of the second last turbine blade which is in turn fluidly connected to a root portion of the last turbine blade through the last heat shield; - a third plurality of inclined radial bores in the last rotor disk for directly supplying cooling air coming from a bore realized inside the bearing cover to the last heat shield.