Creation and study of new forms of matter, such as the Quark Gluon Plasma is an important goal of RHIC and LHC experiments. Heavy quark production and attenuation will provide unique tomographic probes of that matter. We present the predictions of the suppression pattern of open charm and beauty, as well as non-photonic single electrons, in $Au+Au$ collisions at RHIC and LHC energies. The predictions are based on the DGLV (Nucl.Phys.A733:265,2004; Phys.Rev.C68:034914,2003) formalism of radiative energy loss. A cancellation between effects due to the $\sqrt{s}$ energy dependence of the high $p_T$ slope and heavy quark energy loss is predicted to lead to the surprising similarity of heavy quark suppression at RHIC and LHC energies (Phys.Rev.Lett.94:112301,2005).