Plug can get hot from one of two things..
Most common: High resistance and high current
Least: Sunlight shining on it.
One of the things I always do when I pull out the 30 amp cord is clean the blades as they tarnish, resistance builds and it melts.. THEORY has it you should be able to pull 30 amps. Pull more and you get the click of darkness (Breaker trips) but it appears 30 amp plus are not able to handle 30 amps well.
Now.. You said it was tripping the 20 amp branch breaker as well.. True story
My Front A/C was doing that back about Mar/April.. After I verified it waS pulling 21 amps at the point where the breaker broke (tripped) I went topside to see if I could figure out why (had an idea,, I studied engineering after all) pulled top cover, Pulled condenser cover.. Blew crud out with compressed air and soft brush.. Cleaned the rest of it while I was up there.... Replaced covers.. 30 Confirmed a nice 13-14 amps on the meter (it only does units, not tenths and it said 13) for quite some time after I got back inside.. unit is runnign fine since.. To this very minute.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times