An apparatus for extrusion, in particular for extrusion of metal, comprising an extrusion body defining a passage for material to be extruded, including a die having a bearing opening extending between a bearing opening entry surface and a bearing opening exit surface, and wherein cooling means are arranged in the body defining the extrusion passage upstream of the bearing opening exit surface, the cooling means comprising the material of the body being differentiated in thermal conductivity so as to define cooling pathways.