When you say 'back plug' do you mean the female socket end of the power lead that connects into the PC tower? Sounds like a lose connection hence it is heating up the connector, give it a good checking other or at the very least check your property and contens insurance.
Talking about electric kills, I borrowed a hedge trimmer complete with extension cable, of my next door neigbour but one. whist he was getting it, his farther who was there at the time, said always cut away from yourself. Last time I used it I cut right through the cable in two places.
Anyway when I got home and unravelled the extension cable, his dad had put the socket on the lead coming out of the hedge trimmer and the plug on the end of the extension cable. Meaning the extension cable had a plug at both ends!!!!! a lethal death trap if ever I saw one. I warned my neighbour but he seemed non plused, he just popped it back in the garage. you'll never guess his occupation..........he teaches Health and Safety .............honest