The '84s did get bad press about a few Fieros that caught fire (I actually had one do this!).
The problem stemmed from a bad batch of connecting rods. These defective rods would break while driving causing the rod to shoot through the side of the block....the lost oil would hit the hot catalytic converor and, in many cases, take the car with it.
Several years ago I bought an '84 SE with a rod knock to use as parts (my first parts car!) I thought I could limp it home, but not more than 2 miles down the road I threw the rod and it caught fire. Luckily I was able to put the fire out before it engulfed the car.
It is highly likely that your car was either fixed or never had the bad rods to begin with. GM recalled the '84 Fiero and tested them....those with signs of pending doom got new engines.