Besides what's already mentioned, voltage can be part of the issue if you're are running an AC unit. Low volt causes an AC unit to draw more current and then cause more heating at the plug/receptacle connection.
Low voltage is not uncommon and it's worse in the summertime with everyone running AC units and it's in older CGs where it's usually worse. It's a good idea to have a voltmeter to check voltage and best is an LED voltmeter permanently mounted inside. If the voltage gets down to 105 volts, you need to shut the AC off otherwise it will get damaged and without a voltmeter you won't know if this is happening.
If experiencing a hot shore power cord like that, you need to reduce your loads as much as possible until you figure out what is going on.
You should always shut the power off at a pedestal before you plug in otherwise the converter causes pitting on the blades which in turn attracts dirt, leading to a bad plug/pedestal connection and heat.