The large bank of data for ceramics from experiments in flash sintering reveal a surprising characteristic: that the transition to a highly nonlinear rise in electrical conductivity-a signature event for the onset of the flash-occurs within a narrow range of power density. This condition holds for ceramics that are semiconductors, ionic conductors, electronic conductors, and insulators. They flash at temperatures that range from 300 degrees C to 1300 degrees C, and at electric fields from 10 V/cm to over 1000 V/cm. Yet, the power expenditure at the transition for all of them still falls within this narrow range. This, rather uniform value of power dissipation suggests that Joule heating is a key factor in instigating the flash. A general formulation is developed to test if indeed Joule heating alone can lead to the progression of such nonlinear behavior. It is concluded that Joule heating is a necessary but not a sufficient condition for flash sintering.