Thermal instability of a conduction channel in a nonmetallic field emission regime has been assumed as an origin of cathode-initiated vacuum breakdown process. In this article, details are given of a theoretical study of thermal response of a conduction channel in insulating media to de fields, which takes into account the effect of temperature rise on field emission from substrates. It is found that this effect can lead to a regenerative process, which will finally cause a thermal runaway. In addition, an analysis was carried out on chemical vapor deposition diamond films, and it reveals that the thermal conductivity of diamond films is a key parameter in deciding the initiating mechanism of thermal instability of a channel in the film.