Low-temperature scanning tunneling spectroscopy reveals that the Kondo temperature T_K of Co atoms adsorbed on Cu/Co/Cu(100) multilayers varies between 60 K and 134 K as the Cu film thickness decreases from 20 to 5 atomic layers. The observed change
of T_K is attributed to a variation of the density of states at the Fermi level rho_F induced by quantum well states confined to the Cu film. A model calculation based on the quantum oscillations of rho_F at the belly and the neck of the Cu Fermi surface reproduces most of the features in the measured variation of T_K.
