In the large N_c limit of QCD at finite temperature, a new intermediate phase of QCD is predicted. In addition to the hadron phase and the Quark Gluon Plasma, this new intermediate phase has confined glueballs, and the degrees of freedom are consistent with a quasi free quark gas. The new phase is called Quark Spaghetti with Glueballs (SQGB). This phase arises from the hadron phase when using a 3 dimensional string model for QCD. This string theory has no unconstrained parameters. It accurately describes the thermodynamics of quarkless QCD, and as well, QCD with dynamical quarks, precisely reproducing lattice data for T less than 165 MeV for the pressure, energy density and chiral order parameter. In addition, the measured spectrum of massive meson states is accurately described. The Hagedorn limiting temperature for this theory is about 300 MeV, much larger than previously considered. The implications for QCD at finite temperature and baryon density are explored.