We consider an inverse radiation problem of determining the time-varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three-dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is posed as a minimization problem of the least-squares criterion, which is solved by a conjugate gradient method employing the adjoint equation to determine the descent direction. The discrete ordinate S-4 method (M.F. Modest, Radiative Heat Transfer, McGraw-Hill, New York, 1993) is employed to solve the radiative transfer equation and its adjoint equation accurately. The performance of the present technique of inverse analysis is evaluated by several numerical experiments, and it is found to solve the inverse radiation problem accurately without a priori information about the unknown function to be estimated.