Looks to me that at some point the enameled wire on the coil has been broken and someone has soldered it back together... you've got 2 wires twisted and then soldered to another 2 wires. This in effect is creating a short in the windings and so the coil wont be using any of the turns past this bodge up... no wonder its running hot!
If you know the number of turns then rewind it yourself... would be fixed in a morning then. Make sure you wind the coil in the same direction though
