We report the electrical breakdown behavior and subsequent nanogap formation of In(2)O(3)/InO(x) core/shell heterostructure nanowires with substrate-supported and suspended structures. The radial heterostructure nanowires, composed of crystalline In(2)O(3) cores and amorphous In-rich shells, are grown by chemical vapor deposition. As the nanowires broke down, they exhibited two distinct current drops in the current-voltage characteristics. The tips of the broken nanowires were found to have a cone or a volcano shape depending on the width of the nanowire. The shape, the size, and the position of the nanogap depend strongly on the device structure and the nanowire dimensions. The substrate-supported and the suspended devices exhibit distinct breakdown behavior which can be explained by the diffusive thermal transport model. The breakdown temperature of the nanowire is estimated to be about 450 K, close to the melting temperature of indium. We demonstrated the usefulness of this technique by successful fabrication of working pentacene field-effect transistors.