A method for fusing a pair of insulated wires to one another, and a fused wire made by such method, in which the combined or major diameter of the fused wire equals, or very closely matches, the sum of the diameters of the individual wires prior to fusion. In the present method, a pair of wires, each having a coating of insulation that is substantially fully cured, are brought into close abutting contact with one another along a line contact, and thereafter pass through a heating device which heats the coatings above their a thermal transition point of at least one of the pair of wires to fuse the coatings of the wires together along the line contact.