What I did was take a short section of fiberglass sheath like the that used by the theatrical lighting industry. While it may singe over time it will never burn through even with a direct flame appiled.
I then dipped the ends in PlastiDip (like used for your tool handles to make them non-slip) to prevent the ends from fraying apart.
Before I slipped this over the cable I patched up the missing section with Permatex Ultra Black Silicone sealant. This is good for up to 500 degrees.
The photos show the results.

















