If the cord has been pulled on the plug, there may be some broken strands, and thus less wire making the connection, and higher resistance. It is possible to cut the plug off a cord and wire in a new one.

It could also just be that the air conditioning has that high of a current draw that the plug is going to heat up no matter what. My (1500 Watt) blender has a really thick cord, and a well designed plug, but if I run it for 5 minutes the plug gets kinda warm.

Pioneer PDP-5020FD, Marantz SR6011
Axiom M5HP, VP160HP, QS8
Sony PS4, surround backs
-Chris