Your AC draws 11.2 amps at** full voltage**.
Your extension is heating up because it is adding significant resistance to the circuit which drops the voltage.
When the voltage to your AC drops your AC’s compressor will draw more current. Low voltage is bad for your ACs compressor and its quite possibly a hazard to your extension cable (and YOU).
My SWAG is that your extension is the problem, not your breaker.
You should do whatever you can to enable your AC to plug directly into the household’s receptacle. If that is not possible at least get an extension cord that can handle 20 amps. A 12awg (12 gauge) extension can handle 20 amps and will not significantly drop the voltage to your AC. It’s not what I would consider to be a long term solution but it will get you through a hot spell till you can improve your receptacle for use.
I agree with this, this would be my first step, I would also increase the size of the exhaust duct if it has a longer than usual run. Your set up is marginal to start with, anything out of the ordinary could easily become a problem.
Also since the current draw if an air conditioner compressor (which is about 90% of the total for the whole unit, the rest being the fan plus a tiny bit for controls) is tied to the condenser temperature, restricted exhaust tube flow will cause it to use more power. That combined with BubbaDog’s comment about the extension cord could explain why it doesn’t trip the breaker right away, it needs some time to build up pressure and heat for the added resistance of the cord to finally push it over the edge.