We study what happens to the Nucleon, Delta and Omega baryons in the hadronic gas and the quark-gluon plasma, with particular interest in parity doubling and its emergence as the plasma is heated. This is done using simulations of lattice QCD, employing the FASTSUM anisotropic Nf=2+1 ensembles, with four temperatures below and four above the deconfinement transition temperature. Below Tc we find that the positive-parity groundstate masses are largely temperature independent, whereas the negative-parity ones are reduced considerably as the temperature increases. This may be of interest for heavy-ion phenomenology. Close to the transition, the masses are nearly degenerate, in line with the expectation from chiral symmetry restoration. Above Tc we find a clear signal of parity doubling in all three channels, with the effect of the heavier s quark visible.