Natural disasters such as forest fires can result in extensive and costly property damage. These events may be the result of a human error or system failure triggered by electrical discharge, and in such circumstances may form a fulgurite. Understanding fulgurites and their formation may be critical in determining the cause of the fire or other, shock-related event. Here we identify several distinguishing features of fulgurites formed in association with downed power lines, including the presence of melted conductors, transformation of quartz to cristobalite, and morphological differences including increased glass percentage and smaller internal voids. These features are consequences of how heat is transferred to and through a target rock material as it melts and forms a fulgurite, and are predicted from both first principles of diffusive heat transfer, and empirically-derived reaction kinetics for mineral transformations.