We present an X-ray photoemission study of the heavy-fermion system CeCu$_{6-x}$Au$_x$ across the magnetic quantum phase transition of this compound at temperatures above the single-ion Kondo temperature $T_K$. In dependence of the Au concentration $
x$ we observe a sudden change of the $f$-occupation number $n_f$ and the core-hole potential $U_{df}$ at the critical concentration $x_c=0.1$. We interpret these findings in the framework of the single-impurity Anderson model. Our results are in excellent agreement with findings from earlier UPS measurements %cite{klein08qpt} and provide further information about the precursors of quantum criticality at elevated temperatures.
