  We study thermal properties of a large-N massless pion gas using a low-energy
QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build
diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion
mass expansion through an effective vertex that considers all the contributions
coming from closed diagrams. Subsequently, we calculate finite order parameters
such as the quark condensate and its respective derivative, i.e., the scalar
susceptibility, in the chiral limit, along with their associated critical
exponents. These results are compared with our previous unitarized scattering
analyses for the chiral transition universality class, thus showing a
reasonable agreement both with lattice simulations and these resonant studies.
