In ignition theory, there are no volume heat sources in a substance which is being heated through the surface. In most actual cases, ignition occurs under more complex heating conditions. One of these heating conditions is the ignition of a semi-transparent body by the flow of radiant energy. This case is investigated, showing the effect of the presence of volume heat sources of anon-chemical nature on critical and ignition conditions. The Arrhenius heat reaction law and the Frank-Kamenetskii exponential approximation for this law are also used. The ignition characteristics and transition conditions are demonstrated. The transition conditions can be obtained from the condition d theta/d theta(a) = 0, as well as from d(2) psi/d theta(2) = 0. The results show that the critical point in the temperature-time plane can be obtained by setting d theta/d tau = 0, d(2) theta/d tau(2) = 0, and d(3) theta/d tau(3) = 0. The non-stationary solutions are also presented.