power dissipated is more correctly given by H = I^2 RT. a normal wire or gadget has nearly constant resistance. Before short circuit, a little amount of current flows through it which gives minimal power consumption. But during short circuit suddenly large amount of current flows through it for same resistance. So, powderpower dissipated increases too much that it cause fire.
In our normal home circuit we have high resistance in series, in form of inductors and capacitor which does consume negligible energy and almost do not dissipate heat.High resistance means less current. so, like this our device which has normal resistance gets minimal current and work properly. During short circuit let if an inductor is not there , then large current flows through our gadget for its same normal resistance and it burns out.