Modification of the laboratory cross sections for neutron capture on /sup 186/Os and /sup 187/Os caused by the excitation of these target nuclei to a thermal distribution of low-lying nuclear excited states is examined for temperatures appropriate to the stellar s-process (near 30 keV). A correction factor that must be applied to the laboratory values is calculated, ramifications for RE/Os cosmochronology are discussed, and measurements to clarify a highly uncertain situation are suggested.