The problem now is to find the quickest way to get heat energy into the ice. The quickest ways are also very very dangerous and I do not recommend doing them. Transferring large amounts of heat energy in a short amount of time has the usually unpleasant side effect of getting heat energy all over the place where you might not want it (including on yourself).
The very quickest way I can think of to melt a reasonable amount of ice (less than a kilogram, for instance), is to explode