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Conditions for thermal current runaway and breakdown are investigated for the case when the temperature dependence of the electrical conductivity decreases with increasing field. Calculations show that thermal runaway does not arise at fields higher than an upper bound, even though large currents heat the insulator. Conditions found for the absence of thermal runaway are confirmed by experimental observations on silicon nitride. Unless the thermal conductance of the sample is poor and the electrical conductivity unusually large, thermal breakdown is not expected to arise in silicon nitride films.