  The Iterated Perturbation Theory (IPT) equations of the Dynamical Mean Field
Theory (DMFT) for the half-filled Hubbard model, are solved on nearly real
frequencies at various values of the Hubbard parameters $U$, to investigate the
nature of metal-insulator transition (MIT) at finite temperatures. This method
avoids the instabilities associated with the infamous Pad\'e analytic
continuation and reveals fine structures across the MIT at finite temperatures,
which {\em can not be captured} by conventional methods for solving DMFT
equations on Matsubara frequencies. Our method suggests that at finite
temperatures, 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 which
gradually 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 bad
insulator from a true Mott insulator.
