I haven't had an alternator fail on an a/c however I have had one fail on a car. I believe they are of similar design. Your problem sounds like the insulation on part of the windings inside the alternator has failed giving rise to a partial short circuit and hence overheating. The other possibility is that one of the diodes in the rectifier (at the alt' output) has failed, again causing a short circuit.
Needless to say you will need to have an overhauled / new replacement - even if the original cause of the fault was repaired I would not trust it because of the excessive temperature it has been exposed to.
In the case of my example the failure mode was different. The regulator went "funny" (lost normal regulation) and caused the output of the alt' to go up to some 20V or so. The alternator then began to overheat producing that strange hot smell. The vehicle electrics seemed to stand it fortunately (for long enough to get home) but I hate to think of the damage that this could inflict of avionics if it ever happened in the aircraft. I don't think that they have much in the way of protection against long term over-voltage although I am not sure.
Glad you managed to make a safe return to the field. I believe that alternators can produce a fair amount of fumes etc when they fail but don't think they can actually catch fire. I am open to correction on this point though. Once the degree of breakdown had spread past a certain point the dissipation would reduce as the exciter current was lost / reduced (this is normally produced by the alternator, not from an external source). Initially though the regulator action effectively ensures that the overheating is rapid by increasing the excitation - it is trying to maintain the 14V or so output (12V system) in the face of the fault.
Fujiflyer