We examine the high-field operation, power dissipation, and thermal reliability of sorted carbon nanotube network (CNN) devices, with <1% to >99% semiconducting nanotubes. We combine systematic electrical measurements with infrared (IR) thermal imaging and detailed Monte Carlo simulations to study high-field transport up to CNN failure by unzipping-like breakdown. We find that metallic CNNs carry peak current densities up to an order of magnitude greater than semiconducting CNNs at comparable nanotube densities. Metallic CNNs also appear to have a factor of 2 lower intrinsic thermal resistance, suggesting a lower thermal resistance at metallic nanotube junctions. The performance limits and reliability of CNNs depend on their makeup, and could be improved by carefully engineered heat dissipation through the substrate, contacts, and nanotube junctions. These results are essential for optimization of CNN devices on transparent or flexible substrates which typically have very low thermal conductivity.