The invention concerns a turbocharger with variable turbine intake nozzle comprising a mobile cylindrical piston to vary the area of the intake nozzle in the turbine. Vanes mounted on the piston to control the flow into the nozzle penetrate through a slotted heat baffle which supplies a smooth aerodynamic flow into the turbine vanes. The vanes further comprise a stepped portion having greater chord and depth which engage the surface of the heat baffle and hermetically close the slots with the piston in closed position. An axial actuating device is attached to operate the piston.