Thermal Phase Transition in Weakly Interacting Large N_C QCD

We consider thermal QCD in the large N_C limit, mainly in 1+1 dimensions. The gauge coupling is only taken into account to minimal order, by projection onto colour singlets. An expression for the free energy, exact as N_C goes to infinity, is then obtained. A third order phase transition will occur. The critical temperature depends on the ratio N_C/L, where L is the (infinite) spatial length. In the high temperature limit, the free energy will approach the same value as in the free theory, whereas we have a mesonic like phase at low temperature. Expressions for the quark condensate, <\bar\Psi \Psi >, are also obtained.