A survey of the inverse black body radiation problem is presented including a modification to the Hamid-Ragheb approximation which leads to a new approximate formula for the Planck's radiation law valid at all frequencies. The modified regime is useful in solving the inverse black body radiation problem in closed form. The absolute percentage errors in constructing the area-coldness distribution due to the proposed and previous approximations are presented. The results suggest that our modified approximation to Planck's law is more suitable than all other approximations at all frequencies.