Oooh. I have a recent story about this.
I have a long extension cord running from the garage that I plug the trailer into. I have been warned by this forum not to run the AC when connected to 15/20 amps. I do run it on occasion when "camping out" in the driveway with the kids on hot summer nights with no issue.
Until a couple of weekends ago. I was packing the trailer all day on a 90+ degree day and had the AC running all day. When time to leave, I unplugged it and it was VERY hot and pliable, almost melty. I made a note to myself not to ever do this again, and went camping. Also, concerned that if it was that hot, why didn't it trip the breaker?
When I got to the campsite, I pulled out my power cord and removed the 30/15 amp adapter. Or tried to. It was melted stuck. I might have been able to pry it off, but was afraid of damaging it and have no power for the weekend. Luckily at the coast it was 60*, and the AC wasn't needed, so I just plugged into the 15 amp service. I think I dodged some kind of bullet.
What makes things even more frustrating, is that my breaker box at home has a 30A circuit labelled 'travel trailer', but I don't know where the outlet is.