The cross-relaxation rate constants for a three spin system involving hyperpolarized Xe-129, C-13, and H-1 nuclei have been determined over a wide temperature range (136-216 K) through observation of the polarization enhancements from spin polarization induced nuclear Overhauser effect (SPINOE) experiments. A model system of methoxy groups adsorbed on high surface area silica was studied. A maximum polarization enhancement of 3.4 was observed for the methoxy carbon. Xenon-carbon and xenon-proton cross-relaxation were found to be dependent on both the xenon coverage and xenon diffusion across the silica surface. The temperature dependence of the cross-relaxation rate constants was effectively fit using a hopping model. Possible improvements for the SPINOE experiment are suggested including alternative substrates which would retard xenon diffusion across the surface and improve xenon-carbon cross-relaxation leading to significantly larger SPINOE enhancements.