Melting plugs and sheaths on wires happen more often than you might realise.
Poorly terminated wires explain some of them but more often it is due to DIY installations combined with excessive loads being used on the socket.
The first melted plug was connected via a long extension to an outbuiding where the small Consumer unit pitcured was wired directly to it. Multiple freezers were running from it. This really was a fire waiting to happen.
The outdoor socket in the third image shows the sheath melting from the temperatures being reached in the copper cable. The sockets were being used to power extension leads running various outdoor heaters. Again luck was all that had prevented a fire.
Look at the socket calculator here to check whether you're over stressing your cabling and sockets.