A solution method for radiation-conduction transport is developed using complex combination. This method offers an alternative to the direct temporal integration of the transient radiation-conduction equation for problems with periodic boundary conditions, where the sustained solution is of interest. A solution is formulated as an expansion series of temperature fields having frequencies that are multiples of those imposed by the boundary conditions. This series is shown to converge rapidly for most,problems, making it a very efficient technique. (C) 2003 Elsevier Science Ltd. All rights reserved.