  We apply the finite-temperature variational cluster approach to a strongly
correlated and spin-orbit coupled model for four electrons (i.e. two holes) in
the $t_{2g}$ subshell. We focus on parameters suitable for antiferromagnetic
Mott insulators, in particular Ca$_2$RuO$_4$, and identify a crossover from the
low-temperature regime, where spin-orbit coupling is essential, to the
high-temperature regime where it leaves few signatures. The crossover is seen
in one-particle spectra, where $xz$ and $yz$ spectra are almost one dimensional
(as expected for weak spin-orbit coupling) at high temperature. At lower
temperature, where spin-orbit coupling mixes all three orbitals, they become
more two dimensional. However, stronger effects are seen in two-particle
observables like the weight in states with definite onsite angular momentum. We
thus identify the enigmatic intermediate-temperature 'orbital-order phase
transition', which has been reported in various X-ray diffraction and
absorption experiments at $T\approx 260\;K$, as the signature of the onset of
spin-orbital correlations.
