A method for producing a heat pipe comprises the following steps, performed on a first tube made from a malleable material: the diameter of the tube is swaged at a first end, and the end thus swaged is sealed closed; a second tube, of a smaller diameter than the first, is inserted into the second end of the first tube the second end of the first tube is swaged around the second tube and the interface between the two tubes is sealed the pipe thus created is partially filled with a heat-transfer fluid the air contained in the pipe is removed; and the free end of the second tube is sealed closed.