Though I've never heard of a fire but I have seen minor explosions in distributors where the cap was 'blown up'/shattered. Oil fumes, usually gas laden, would get in there from very worn bearings. Then the spark, either from points making and breaking contact or the rotor gap to tower contact arc would light it off once it reached the correct concentration. It sounds like a prime time to take that distributor out, carry in-hand to the dumpster and then update with an electronic ignition system and enjoy much less maintenance, easier starting and better gas mileage. If you are trying to maintain the OEM appearance, then there are those distributors available as well.

As a new guy, welcome als o let us know what you did to 'fix' the problem