If you wire was bare due to heat stress, your wire is intrinsically compromised. It probably has broken strands at every bend. Also if bare and left unprotected for any length of time, you have corrosion. Best to replace it from end to end.
Also if this is going to be a heat related issue, I would after installing the new wire, use heat shrink over your wire. You can heat the heatshrink to mold with your wire with a hair dryer. Also you can use GLASS tape to finally wrap the wire and heat shrink. Glass tape is very resistant to heat, and commonly used for thermo-couples in heated dies.
Heat shrink commonly found at electrical supply house, for about 50 cents a ft. and the glass tape is several bucks a roll, but worth every penny.
Should you want to go all out, they make a heatshrink especially for heated applications.