A method and an extrusion device for producing a foamed body. A plastics melt is produced inside the casing of a first extruder. The plastics melt is conveyed to an outlet die of a second extruder. The conveyed plastics melt has a foaming agent and expands after being fed through the outlet die. Before the plastics melt is fed through the outlet die, variations in temperature between different radial positions over the cross-section of the plastics melt are reduced by an extruder screw device which has a number of screw spindles distributed around the periphery. The plastics melt which is thus thermally homogeneous is fed through the outlet die.