A set of numerical computations of the thermal structure and optical luminosity of strong shock waves in air is described. The model includes radiation transport coupled with hydrodynamics under assumed conditions of steady flow. With shock velocities above 10 km/sec a thermal precursor develops ahead of the shock front, and increases in prominence with increasing shock strength. For velocities above 50 km/sec the precursor is partially opaque to visible light and the computed brightness is smaller than that of a blackbody at the shock temperature. At higher velocities the brightness decreases with increasing shock strength. Steady solutions could not be found for velocities above 80 km/sec.