Energy-stability theory is applied to the case of radiation heat transfer in an optically thin, quiescent fluid layer heated from below and bounded by rigid, black, perfectly conducting planes. The radiation term in the energy equation destroys the quadratic character of the energy identity. It is shown, however, that the right-hand side of the energy identity can be bounded by a suitable quadratic term for al physically allowable disturbances. The result is a conditional stability limit dependent upon disturbance amplitude. Results are computed for a variety of cases; these are compared to existing linear and energy stability results.