Electrical short circuits are pretty brief in duration. Like 5 milliseconds. Now overloaded circuits with oversized fuses or breakers will heat up the wiring until it (the wire) becomes the fuse.
I've seen that happen. High power audio amplifiers in cars, installed by chimps who placed the proper 50 amp fuse near the amplifier and not right next to the battery. The 10 gauge wire from the positive terminal gets sliced open by the seat track/rail and becomes a light bulb filament.
Oooh oooh that smell.