  Dependence of transport coefficients of the Yb(Rh$_{1-x}$Co$_x$)$_2$Si$_2$
series of alloys on temperature and cobalt concentration is explained by an
asymmetric Anderson model which takes into account the exchange scattering of
conduction electrons on ytterbium ions and the splitting of 4$f$-states by the
crystalline electric field (CEF). The substitution of rhodium by cobalt is
described as an increase of chemical pressure which reduces the exchange
coupling and the CEF splitting. The scaling analysis and numerical NCA solution
of the model show that the effective degeneracy of the 4$f$-state at a given
temperature depends on the relative magnitude of the Kondo scale and the CEF
splitting. Thus, we find that dependence of the thermopower, $S(T)$, on
temperature and cobalt concentration can be understood as an interplay of
quantum fluctuations, driven by the Kondo effect, and thermal fluctuations,
which favor a uniform occupation of the CEF states. The theoretical model
captures all the qualitative features of the experimental data and it explains
the evolution of the shape of $S(T)$ with the increase of cobalt concentration.
