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The thermodynamics of massless ideal gas of overlap quarks has beeninvestigated numerically for both zero and nonzero baryon chemical potential$\mu$. While the parameter M has been shown to be irrelevant in the continuumlimit, it is shown numerically that the continuum limit can be reached withrelatively coarser lattices for certain range of M. Numerical limitation of theexisting method of introduction of chemical potential in the overlap formalismis discussed. We have also studied the energy density of free domain wallfermions in the absence of $\mu$ and estimated the extent of lattice in thefifth dimension $L_5$ for which the overlap results are recovered.Interestingly, this value of $L_5$ is also minimum for the same range of Mfound in the overlap case.

Towards QCD thermodynamics using exact chiral symmetry on lattice