Heat transfer in a radiatively participating medium involves higher coupling than is typical for pure conduction and/or convection problems. Consequently, standard discretizing techniques such as partitioning regions of a finite volume domain on separate processors are inefficient. Additionally, standard angular decompositions may introduce discontinuities into the solution which are difficult to model accurately. A scalable method for parallelizing the radiative transport equation is presented. A standard discrete ordinates formulation is used to transform the integro-differential equation into a system of partial differential equations. The resulting system of equations is then solved by an optimal grid-independent, sequential-function approach that captures discontinuities accurately without additional user interaction. Results for one- and two-dimensional cases are given.