  Properties of QCD matter change significantly around the chiral crossover
temperature, and the effects on $U(1)_A$ and topological susceptibilities, as
well as the meson spectrum have been studied with much care. Baryons and the
effect of parity doubling in this temperature range have been analyzed
previously by various other groups employing different setups. Here we
construct suitable operators to investigate chiral and axial $U(1)_A$
symmetries in the baryon spectrum. Measurements for different volumes and
quark-masses are done with two flavors of chirally symmetric domain-wall
fermions at temperatures above the critical one. The possibility of emergent
$SU(4)$ and $SU(2)_{CS}$ symmetries is discussed.
