Reconnecting a burned or broken wire without finding the cause of the damage only sets the stage for another failure. Each wire in a range was selected to withstand normal amounts of current and heat without degrading. If a wire or connection breaks from overheating, an electrical fault probably overloaded the circuit. If you lack the expertise to troubleshoot the range and replace the faulty part, ask a qualified technician for advice before continuing the repair. Some manufacturers offer range owners detailed troubleshooting procedures, but hiring a trained professional puts the range back in safe operating condition quickly.
Wires in a range seldom fail due to mechanical stress. Many parts of the system use stranded wiring that resists fatigue faults better than solid conductor wiring. A wiring harness consists of many wires cut to exact lengths, each selected for a specific temperature range and voltage. Broken wires might not have enough slack to splice without straining the new connection. Putting tension on any wire in the harness can cause a mechanical failure or possibly shift wires out of safe locations. Replacing a broken wire with a new wire rated for the same conditions makes a more dependable repair.
Ceramic wire nuts make splicing wires easy, and their maximum working temperature of 1,000 degrees F. easily exceeds the highest temperature of a range. When installed properly, wire nuts create a durable connection with excellent conductivity. Sloppy wire nut splices might place enough electrical resistance in the connection to cause problems in both gas and electric ranges. Wire nut splices don't match the strength of the original wire, but perform well where the wire doesn't undergo mechanical strain. Don't use wire nuts to splice a taut wire without installing a strain-relief to take the load.
Stripping wire insulation with a pocket knife damages the conductor and can cause broken splices and electrical shorts. Use a wire stripper to strip an inch of insulation from each wire's end. Twist stranded conductors clockwise by hand to keep the wire bundles neatly together. Hold the conductors parallel and grip the ends with electrician's pliers, twisting clockwise at least four turns. A good pigtail splice shows no gaps between conductors. Select a ceramic wire nut to match the wire gauge and thread the nut onto the pigtail tightly, by hand. Twisting the insulated portion of the wiring for two or three more turns adds some mechanical strength.