Your extension chord sounds like it belongs in the trash. An inadequate or faulty extension chord is potentially dangerous and can overheat or reduce the service life of some appliances or tools, like your air compressor.
Any time an extension chord or plug gets more than a little warm you have a problem. Not only are you risking damaging any tool you plug into the extension chord, you are literally playing with fire. Electrical fires are almost never caused by faulty house or shop wiring; they are almost always caused by faulty extension chords or faulty electrical appliances.
What is the gauge of the extension chord? "Heavy duty" can mean it's only 16 gauge; 14 gauge is the absolute minimum for a shop extension chord. I bet if you read your air compressor's owner's manual, it will say "no extension chords" or "12 gauge minimum." Best to heed this advice.
Moral of the story, you aren't saving a buck in the long run using a cheap or inadequate extension chord to run tools like an air compressor.
You are the one you've been waiting for.