If you can get spark from the wire, but not the plug, I'd suggest a bad plug (I'm sure you're already there). I'm thinking the coil may be getting hot due to your method of inciting the spark ... I'd replace the plug, then see if it's getting hot still. A coil really doesn't cost that much so replacing it may be a simple fix to all of this.
I've tried with a brand new plug, still no spark.
I didn't think of seeing if it heated up with it, though. I'll go check that.
Also, if you are not seeing the spark jump the electrode of the plug, try holding the plug body the 1mm from the frame and see if you get a spark that way ... It wouldn't be the first time I'd have seen a bad plug right out of the box.
Good point. Confirmed your suspicion: the ignition coil does not heat up when the spark plug is installed correctly, even after several 10 second cranking sessions.
Based on blog.lawneq.com/how-to-check-the-ignition-coil-on-your-mower, I think my ignition coil is faulty.
Spark plug seems to be good, BTW
With a regular coil, you should be able to check resistances within the coil and tell if it's bad or not. If the test which was provided through that web page is showing you a fault, you should be golden. Now that I think about it, I believe coil heating can also be a sign of failure (internal continuity or something), where the spark energy is feeding back through the coils. While it may provide an air gap spark, when you introduce the resistor plug, there may not be enough juice to jump the gap.