  A lagrangian for gauge fields coupled to fermions with the Kac-Moody group as
its gauge group yields, for the pure fermions sector, an ideal gas of Kac-Moody
fermions. The canonical partition function for the $\hat U(1)$ case is shown to
have a maximum temperature $kT_{M} = |\lambda| /\pi$, where $\lambda $ is the
coupling of the super charge operator $G_0 $ to the fermions. This result is
similar to the case of strings but unlike strings the result is obtained from a
well-defined lagrangian.
