In a method of melting together axial ends of bunched fibers of thermoplastic material, the fiber ends are brought into contact with the heated surface of a stamp. The body of the stamp is heated by controlling an electric current passing through it. In one embodiment the stamp is cooled by a flow of compressed air before the stamp is separated from the fiber ends. In another embodiment, the stamp is separated from the melted fiber ends, heated to a higher temperature to vaporize any residual fiber material, and cooled by exposure to compressed air until it has no more than the temperature for melting the fiber material.