The Bureau of Mines has developed a time-dependent mathematical model of radiative heating of bulkheads in mines. The model includes both reradiation from the duct (cylindrical) walls and direct radiation from the fire zone. Thermal loss into the wall of the duct and into the bulkhead is included. Both brick and wood bulkheads are considered. It is found that the heating rate of the system scales as the duct length-to-diameter ratio and the flame temperature. In particular, the time required for the irradiated surface of the bulkhead to reach a specified temperature decreases with increasing flame temperature for a fixed length-to-diameter ratio and increases with increasing length-to-diameter ratio for a specified flame temperature. It is also determined that the time, t, for the bulkhead surface temperature to reach a specific value, tb, for a fixed length-to-diameter ratio less than 4 and for a flame temperature of 1,200 k is approximately linearly dependent on tb for 500 k < tb < 700 k, and is nearly exponentially dependent on the length-to-diameter ratio for tb = 600 and 700 k.