What he said, 100%. It’s nothing to do with inductance whatsoever. Everyone says that but it’s a myth. It’s resistive heat generated which builds up in the reel. When cable is extended, the exact same heat is dissipated, but it’s spread out across the length of the cable.
Back to the OP. I bet the Very hot pin he was referring to was not the one on the actual granny plug itself but the one on the extension lead plug? Also, I bet it was the L pin?
Its very often caused by crap (resistive) connection to the 13A fuse end caps. It can be due to old oxidised fuse caps, or fuse holder clips. Also the fuse holder clips often have inadequate tension onto the actual fuse. What happens then is they can heat up, which then causes even less tension and even more contact resistance and even more heating. Before you know it the plug can self destruct with a kind of thermal runaway.
Another cause of heating pins is lack of contact tension in the wall socket, possibly combined with old oxidised mating surfaces on plug pins and contact clips in the socket. Then add to that gradually self loosening screw terminals and even solder tinned stranded wire ends which is a really big no no, yet often seen. Even an ageing or poor quality 13A fuse can cause heating on its own.
Sadly our so called 13A plug and socket system isn’t great, and often cannot safely handle it’s rated current continuously. This is then made even worse with lots of inferior imported units and a complete lack of proper type approvals or regulation. I’ve seen lots of heat damaged 13A plugs, sockets and adapters etc in my time.
With a bit of TLC they can be made to work ok at full load, but need regular checking and maintenance which they rarely (if ever) get. Peter