Charret et al. applied the properties of Grassmann generators to develop a
new method to calculate the coefficientes of the high temperature expansion
of the grand canonical partition function of self-interacting fermionic mo
dels on d-dimensions (d greater than or equal to 1). The method explores th
e anti-commuting nature of fermionic fields and avoids the calculation of t
he fermionic path integral. We apply this new method to the relativistic fr
ee Dirac fermions and recover the known results in the literature without t
he beta-independent and mu-independent infinities that plague the continuum
path integral formulation.