We present the analysis of the X-ray brightness and temperature profiles for six clusters belonging to both the Cool Core (CC) and Non Cool Core (NCC) classes, in terms of the Supermodel (SM) developed by Cavaliere et al. Based on the gravitational wells set by the dark matter (DM) halos, the SM straightforwardly expresses the equilibrium of the intracluster plasma (ICP) modulated by the entropy deposited at the boundary by standing shocks from gravitational accretion, and injected at the center by outgoing blast waves from mergers or from outbursts of active galactic nuclei. The cluster set analyzed here highlights not only how simply the SM represents the main dichotomy CC versus NCC clusters in terms of a few ICP parameters governing the radial entropy run, but also how accurately it fits even complex brightness and temperature profiles. For CC clusters like A2199 and A2597, the SM with a low level of central entropy straightforwardly yields the characteristic peaked profile of the temperature marked by a decline toward the center, without requiring currently strong radiative cooling and high mass deposition rates. NCC clusters like A1656 require instead a central entropy floor of a substantial level, and some like A2256 and even more A644 feature structured temperature profiles that also call for a definite floor extension; in such conditions the SM accurately fits the observations, and suggests that in these clusters the ICP has been just remolded by a merger event, in the way of a remnant cool core. The SM also predicts that DM halos with high concentration should correlate with flatter entropy profiles and steeper brightness in the outskirts; this is indeed the case with A1689, for which from X-rays we find concentration values c ∼ 10, the hallmark of an early halo formation. Thus, we show the SM to constitute a fast tool not only to provide wide libraries of accurate fits to X-ray temperature and density profiles, but also to retrieve from the ICP archives specific information concerning the physical histories of DM and baryons in the inner and the outer cluster regions.