Mark knows his stuff but as the block is cool to touch and the fan is still running could I suggest you have a look at the fan control relay. Not common but not unknown for a relay to have its contacts welded shut. If your car has a fan switch in the radiator might be worth pulling the wires off and if you have an Ohm meter checking to see if it's closed circuit, it should be open circuit when cold/cool.
BR
Colin
