sorry it took me a minute to post, so now that its the receptacle that is overheating. you could try to put the air conditioner in another room and run it for a little bit, see if that receptacle heats up. if it does then that is a good indication that your air conditioner is drawing more power than the wire in the house was designed for. do you know what size of wiring is in the house? did you notice when you replaced the receptacle? 12 gauge is rated for 23 amps. you will need to see what the rating on the air conditioner is..

depending on the age of the apt she's in, it might not have an adequate electrical system.