Covariant Thermodynamics and ``Realistic'' Friedmann Model

We discuss a cosmological Friedmann model modified by inclusion of off-shell matter which has an equation of state $p,\rho \propto T^5,$ $p=1/4\rho .$ Such matter is shown to have energy density comparable with that of non-interacting radiation at temperatures of the order of the Hagedorn temperature, $\sim 10^{12}$ K, indicating the possibility of a phase transition. It is argued that the $T^5$-phase, or an admixture, lies below the high-temperature $T^4$-phase.