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 models on d-dimensions (d > or = 1). The method explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. We apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the beta-independent and mu-independent infinities that plague the continuum path integral formulation.