Simulations have been performed to determine the internal temperature profiles of high-power GaAs photoconductive switches in the presence of a current filament. No thermal instability is predicted below a power generation density level of about 1.3 ×1014 W/m3. This prediction is in keeping with recent experimental data on photoconductive semiconductor switch devices. It is shown that this power dissipation density threshold for stability exists under both dc and transient conditions. A simple model provides qualitative support for the power density threshold, and an explanation of the filamentary current radii that have been observed experimentally.