Linear sigma model with parity doubling

Recent lattice-gauge-theory simulations at finite temperatures have suggested that chiral-symmetry restoration at finite temperatures entails parity doubling of the baryon spectrum. We show that a natural extension of the Gell-Mann--L\'evy model incorporates this effect. Predictions of this candidate effective model for the hadronic component of high-density and high-temperature nuclear matter are discussed. The model suggests a parametrization of the dependence of the baryon-doublet masses on the quark mass. This parametrization is compared with the recent lattice results.