Ultra-violet angle-resolved photoemission spectroscopy (UV-ARPES) was used to explore the temperature dependence of the Ce-4fspectral responses for surface and bulk in the antiferromagnetic Kondo lattice CeRh2Si2. Spectra were taken from Ce- and Si-terminated surfaces in a wide temperature range, and reveal characteristic 4fpatterns for weakly (surface) and strongly (bulk) hybridized Ce, respectively. The temperature dependence of the Fermi level peak differs strongly for both cases implying that the effective Kondo temperature at the surface and bulk can be rather distinct. The greatly reduced crystal-electric-field (CEF) splitting at the surface gives reason to believe that the surface may exhibit a larger effective Kondo temperature because of a higher local-moment effective degeneracy. Further, the hybridization processes could strongly affect the 4fpeak intensity at the Fermi level. We derived thek-resolved dispersion of the Kondo peak which is also found to be distinct due to different sets of itinerant bands to which the 4fstates of surface and bulk Ce are coupled. Overall our study brings into reach the ultimate goal of quantitatively testing many-body theories that link spectroscopy and transport properties, for both the bulk and the surface, separately. It also allows for a direct insight into the broader problem of Kondo lattices with two different local-moment sublattices, providing some understanding of why the cross-talking between the two Kondo effects is weak.