Any car thats this old not taken care off has a high possibility of igniting. The 84's had weak engine rods, so if you let the oil get old, or low, the rod would snap through the block, spewing hot oil all over the catalytic convertor, which caught it on fire. Later models didn't have as much of a problem, but they did burn up, on V6's if the front manifold is leaking (The hardest one to get to) can cause a fire cause they tend to leak. The main fires were from oil getting on something hot and igniting. Other sources of fire were the wiring. Nowadays you should clean all the old dry leaves out of the engine compartment, pull the heater thing in the front, and pull the leaves, or that can catch on fire. make sure your heat shields are over all the places where it should be, and make sure your cat or straight pipe (if you have one) has a shield over it. Etc.
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In Progress Restoration/Hot Rodding of a 1984 SE, to be powered by some sort of motor from the GM Line.
Future owner of an 84 SE converted with 86 GT parts, and 50,000 mile V6
Star Wars: Knights of the Old Republic, Friggen ROCKS on Xbox, you must buy it and an xbox if you don't have one, its worth getting the system for this game.