Cooling system for gas turbine and method for cooling a gas turbine

The cooling system (42) includes an axial annular channel containing a crown of compressor guide blades (14, 28), and a crown of guide blades (16) fixed to a rotor disk (19) of the rotor (3). The input line has a part channel (44) which passes through at least one of the blades (28) of the crown, with an aperture (48, 49) to allow the fluid (45) out is connected in the region of the cooling air outlet point (34).