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The crystal-field ground state wave function of CeCu₂Si₂ has been investigated with linear polarized M-edge x-ray absorption spectroscopy from 250 mK to 250 K, thus covering the superconducting (T_c = 0.6 K), the Kondo (T_K ≈ 20 K) 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 Γ₇⁽¹⁾ crystal-field ground state and the thermal population of excited states at around 30 meV. 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 4f ⁰ configuration in the ground state is consistent with the possibility of 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 Γ₆ state and Γ₇⁽²⁾ crystal-field states are mixed into the primarily Γ₇⁽¹⁾ ground state. This estimate is also supported by re-normalized band-structure calculations that use the experimentally determined crystal-field scheme.