Some additional comments: The air conditinoers in my motor home normally run on 20 amp branch circuits no matter what I"m plugged into. (that is how they were wired at the factory) Right now the one I'm using is running on the park's 20 amp, it's isolated from the rest of the coach electrically. (has it's own plug which can be plugged into the coach)
In re-reading the Original post it was not the extension cord (Which likely was too light weight for a sustained 20 amp load) but the adapter that caught fire.. Now that is supposed to be 30 amp (heavier) wire.. So it had to be defective or worn out for this to have happened. I gave an example of defect in my last post.
I have noticed over time teh plastic around the pins, epically the hot pin, gets discolored indicating high heat.. I do not know why it's the hot pin since in theory, they both carry the same current.
In a 15 amp outlet, I'd know why (The neutral pin is heavier than the hot)