  Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy
analog($S^2_F$) come paired with anticommuting chirality operators. A
consequence of this is seen in the fermion-like spectrum of these operators
which is especially true even for the case of integer-spin Dirac operators.
Motivated by this feature of the spectrum of a spin 1 Dirac operator on
$S_F^2$, we assume the spin 1 particles obey Fermi-Dirac statistics. This
choice is inspite of the lack of a well defined spin-statistics relation on a
compact surface such as $S^2$. The specific heats are computed in the cases of
the spin $\frac{1}{2}$ and spin 1 Dirac operators. Remarkably the specific heat
for a system of spin $\frac{1}{2}$ particles is more than that of the spin 1
case, though the number of degrees of freedom is more in the case of spin 1
particles. The reason for this is inferred through a study of the spectrums of
the Dirac operators in both the cases. The zero modes of the spin 1 Dirac
operator is studied as a function of the cut-off angular momentum $L$ and is
found to follow a simple power law. This number is such that the number of
states with positive energy for the spin 1 and spin $\frac{1}{2}$ system become
comparable. Remarks are made about the spectrums of higher spin Dirac operators
as well through a study of their zero-modes and the variation of their spectrum
with degeneracy. The mean energy as a function of temperature is studied in
both the spin $\frac{1}{2}$ and spin 1 cases. They are found to deviate from
the standard ideal gas law in 2+1 dimensions.
