We determine Zr and Nb elemental abundances in barium stars to probe the operation temperature of the s-process that occurred in the companion asymptotic giant branch (AGB) stars. Along with Zr and Nb, we derive the abundances of a large number of heavy elements. They provide constraints on the s-process operation temperature and therefore on the s-process neutron source. The results are then compared with stellar evolution and nucleosynthesis models. We compare the nucleosynthetic profile of the present sample stars with those of CEMP-s, CEMP-rs and CEMP-r stars. One barium star of our sample is potentially identified as the highest-metallicity CEMP-rs star yet discovered.