Fire spread in wildland fuels is modeled as the steady, longitudinal propagation of an isothermal surface at ignition temperature by the process of radiation transport through a uniform layer of randomly-distributed, thermally-thin, radiometrically-black fuel particles. The ignition isotherm is assumed to be a perfect diffuse radiator, as is the idealized planar flame sheet that stands above the fuel bed. An algorithm is described that finds the temperature field everywhere in the fuel bed, the shape of the ignition isotherm, and the fire spread rate. The fire spread rate, multiplied by the heat required to ignite a unit volume of the fuel bed, divided by the hemispherical power flux density from the ignition isotherm, is an eigenvalue of this problem. The approximation of unit emissivity for fuel particles is shown to be robust in the one-dimensional limiting case of an infinitely-deep fuel bed. This limiting case is solved by a different algorithm that takes advantage of the axial symmetry of the radiation intensity field and allows explicit use of the scattering function for randomly-oriented, convex, radiometrically gray, diffuse scattering particles. It is shown that the temperature field is insensitive to particle emissivity for emissivity greater than 0.7 in this limit. ('This manuscript was written and prepared by an employee of the U.S. Government on official time and is therefore in the public domain.')