A variational procedure for calculating thermal cross sections and diffusion theory parameters is described. The method permits the calculation of an approximate lethargy-dependent Wigner Wilkins flux spectrum for a region as a linear combination of two lethargy- and temperature-dependent base spectra. The coefficients for linearly combining the base spectra are provided by the theory and once the coefficients are calculated the flux is determined. The average microscopic cross sections and diffusion theory parameters for the region are calculated from a flux weighted average of lethargy-dependent microscopic cross sections and diffusion constants. Cross sections and diffusion theory parameters calculated in this manner agree well with those obtained from the SOFOCATE code.