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The Iterated Perturbation Theory (IPT) equations of the Dynamical Mean FieldTheory (DMFT) for the half-filled Hubbard model, are solved on nearly realfrequencies at various values of the Hubbard parameters $U$, to investigate thenature of metal-insulator transition (MIT) at finite temperatures. This methodavoids the instabilities associated with the infamous Pad\'e analyticcontinuation and reveals fine structures across the MIT at finite temperatures,which {\em can not be captured} by conventional methods for solving DMFTequations on Matsubara frequencies. Our method suggests that at finitetemperatures, there is an abrupt decrease in the height of the quasi-particle(Kondo) peak at a critical value of $U_c$, to a non-zero but small bump whichgradually suppresses as one moves deeper into the {\em bad} insulator regime.In contrast to Vollhardt and coworkers [J. Phys. Soc. Jpn. {\bf 74} (2005)136], down to $T=0.01$ of the half-bandwidth we find no $T^*$ separating badinsulator from a true Mott insulator.

Dynamical Mean Field Theory equations on nearly real frequency axis