UK Car Repair: catalyst converter overheat, rolls royce silver shadow, royce silver shadow

Question
I have a 1980 Rolls Royce Silver Shadow II and lately the driver-side catalyst converter overheats. The floor board on the driver side gets extremely hot after a few minutes of driving. So hot that it burned the mat. The car run very good, so I don't think excess fuel is being unburned and therefore dumped into the converter. I don't think its the oxygen sensor either, but not sure. I suspesion is the the honeycones has shifted in that converter. The car has 65,000 miles. Any suggestions?

Answer
This was a common problem on the cars, when they were new we removed the convertors and re-insulated the underfloor, on many cars the carpets were very badly burned. Your diagnosis is correct it is caused by overfueling, most likely a cylinder misfiring.  If you remove the plugs on that side you can tell which is the bad cylinder.  You can then do some testing to see why it isn't firing. Oftren, if the overheating is prolonged it can melt the catalyst and block the exhaust.