  We compute the screening masses of fields with nucleon quantum numbers for a
wide range of temperatures between $T \sim 1$ GeV and $T\sim 160$ GeV. The
computation has been performed by means of Monte Carlo simulations of lattice
QCD with $N_f=3$ flavors of $O(a)$-improved Wilson fermions: we exploit a novel
strategy which has recently allowed to determine for the first time non-singlet
mesonic screening masses up to extremely high temperatures. The baryonic
screening masses are measured with a few per-mille precision in the continuum
limit, and percent deviations from the free theory result $3\pi T$ are clearly
visible even at the highest temperatures. The observed degeneracy of the
positive and negative parity state's screening mass, expected from Ward
identities associated to non-singlet axial transformations, provides further
evidence for the restoration of chiral symmetry in the high temperature regime
of QCD.
