The anomalous low temperature suppression of the spin accumulation signal ΔRNL in non-local spin valves (NLSVs) based on common ferromagnet (FM)/normal metal (N) pairings has recently been shown to result from a manifestation of the Kondo effect. Local magnetic moments in the N due to even minor levels of FM/N interdiffusion depolarize the injected spin current, suppressing the effective spin polarization around and below the Kondo temperature TK. Previous studies have focused on FM/N combinations that happen to have low TK so that Kondo effects occur only well below 300 K. Here, we study NLSVs based on Co/Cu, a materials combination that is not only technologically relevant but also has a high TK, up to 500 K. Despite the negligible equilibrium solubility of Co in Cu, we find clear Kondo effects in both ΔRNL and Cu resistivity, due to Co/Cu intermixing that we probe via quantitative transmission electron microscopy. Most significantly, under certain conditions the spin Kondo effect suppresses the injected spin polarization even at room temperature, with important technological implications. Studies as a function of the Cu thickness and annealing temperature reveal complex trends in interdiffusion lengths and Kondo effects, which we interpret in terms of the interplay between diffusion kinetics and thermodynamics, as well as the thickness dependence of the Kondo effect.