Abstract: A turbine-nozzle vane fitted with a cooling system including a hollow airfoil (45) inserted between an outer deck and an inner deck (46). Disposed inside the airfoil (45) is a liner (60) which is fitted with a multi-perforated skirt to impact-cool the airfoil wall. The liner (60) has an inner wall (62) comprising a female frustum of a cone (66). A male frustum of a cone (64) is rigidly affixed to the inner deck (46) and is nested in the female frustum (66). These frusta provide communication between the inside of the liner (60) and the inside of the inner deck (46). Cooling air (70) is introduced into the liner (60) through the outer deck. A portion (71) of this air impact-cools the airfoil wall. Another portion (72) enters the inner deck (46) and passes through an orifice (67) to cool the turbine disks (49, 50) upstream and downstream of the nozzle.