No, fire is reserved for a catastrophic part failure, which would be due to a manufacturing defect (or wiring the "turbo" button on your 486 case to the "reset" jumper on the 486 mobo, but that's another story). Because of that, leaving the computer on is very unlikely to cause a fire. Of course if you had a G4 cube and duct taped over all the vents while cracking RC5, you might get a lot of smoke and a bad smell.
Zenmervolt