A machine for manufacturing, by coextrusion, a profiled element strip based on a plurality of extruded strips made of elastomeric compounds, comprising an extrusion head having flow ducts, inlet orifices of which are connected to outlets of at least two extruders for supplying extruded strips made of elastomeric compounds, and outlet orifices of which lead into a die which is adjacent to a roller and is designed to cooperate with the roller to shape the profiled element strip, the roller having a central axis surrounded by an external surface intended to receive the profiled element strip and a driver for driving the roller in rotation about its central axis, wherein the flow ducts are mutually parallel and are perpendicular to the circumferential direction of the roller, and the profiled element strip is joined to the external surface of the roller along an equivalent length of at least 700 mm, wherein the machine includes a first cooling surface for the external surface of the roller and a second cooling system for support bearings of the roller, the first and second cooling systems being connected to a control unit which controls the operation of the first and second cooling systems according to a same setpoint temperature.