  The crystal-field ground state wave function of CeCu$_2$Si$_2$ has been
investigated with linear polarized $M$-edge x-ray absorption spectroscopy from
250mK to 250K, thus covering the superconducting ($T_{\text{c}}$=0.6K), the
Kondo ($T_{\text{K}}$$\approx$20K) as well as the Curie-Weiss regime. The
comparison with full-multiplet calculations shows that the temperature
dependence of the experimental linear dichroism is well explained with a
$\Gamma_7^{(1)}$ crystal-field ground-state and the thermal population of
excited states at around 30meV. The crystal-field scheme does not change
throughout the entire temperature range thus making the scenario of orbital
switching unlikely. Spectroscopic evidence for the presence of the Ce 4$f^0$
configuration in the ground state is consistent with the possibility for a
multi-orbital character of the ground state. We estimate from the Kondo
temperature and crystal-field splitting energies that several percents of the
higher lying $\Gamma_6$ state and $\Gamma_7^{(2)}$ crystal-field states are
mixed into the primarily $\Gamma_7^{(1)}$ ground state. This estimate is also
supported by re-normalized band-structure calculations that uses the
experimentally determined crystal-field scheme.
