Extension Cord Fried

The specific damage to that cord was not caused by the gauge of the wire. That is arcing damage, and it's caused by a poor connection inside the cord end.
However, you shouldn't use a 16 gauge 50 foot cord with anything much more powerful than a fan or trouble light. For a hot air gun or similar, you should use at least a 14 gauge cord, and 12 would be better. If you dropped to a 25 foot cord, then 14 gauge would be fine.