  Studying various thermodynamic quantities for the free domain wall fermions
for both finite and infinite fifth dimensional extent N_5, we find that the
lattice corrections are minimum for $N_T\geq10$ for both energy density and
susceptibility, for its irrelevant parameter M in the range 1.45-1.50. The
correction terms are, however, quite large for small lattice sizes of
$N_T\leq8$. We propose modifications of the domain wall operator, as well as
the overlap operator, to reduce the finite cut-off effects to within 10% of the
continuum results of the thermodynamic quantities for the currently used
N_T=6-8 lattices. Incorporating chemical potential, we show that \mu^2
divergences are absent for a large class of such domain wall fermion actions
although the chiral symmetry is broken for $\mu\neq0$.
