The invention relates to an extrusion die (30) which includes at least one insert (31, 32) for shaping a material to be extruded pushed through the die, said insert being tubular, being centred on an axis (X31, X32), and having both an upstream end (31A, 32A), via which the material enters the insert, and a downstream end (31B, 32B), via which the material exits to the outside of the extrusion die. In order for said extrusion die to make it possible, even with a modest flow of extruded material, to obtain large extruded products having a regular surface, it is provided for the material to flow in a cylindrical channel (C31, C32) of the insert, connecting the upstream and downstream ends thereof, which has a substantially constant cross section between a pre-expansion diaphragm located at the upstream end, not included, and the downstream end, included. The diaphragm defines a through-opening (O37, O38), substantially centred on the axis (X31, X32) and having a smaller cross section than that of the channel, so that, before flowing in the channel, the material entering the insert passes through the diaphragm, undergoing a loss of load which, at the outlet of the diaphragm, pre-expands the material by distributing same homogeneously over the entire inner periphery of the channel. Moreover, the extrusion die includes means (310, 320) for controlled heating of the insert, suitable for keeping the temperature of the material pre-expanded by the diaphragm substantially homogeneous along the channel of the insert.
