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Studying the charmed hadron production is a particularly useful tool to probe properties of hot and dense matter created in ultrarelativistic heavy ion collisions. It allows one also to extract the information about mechanisms of in-medium heavy quark thermalization. In this talk, the phenomenological analysis of various characteristics of charmed hadrons (J/Psi and D mesons) in heavy ion collisions at RHIC and LHC has been done in the frameworks of two-component HYDJET++ model. Among other heavy ion event generators, HYDJET++ focuses on the detailed simulation of jet quenching effect taking into account medium-induced radiative and collisional partonic energy loss (hard "non-thermal" component), and also reproducing the main features of nuclear collective dynamics by the parametrization of relativistic hydrodynamics with preset freeze-out conditions (soft "thermal" component). The charmed meson production pattern in heavy ion collisions at RHIC and LHC is reproduced by HYDJET++ simulations. The possibility of thermalization of J/Psi and D mesons at RHIC and LHC energies is discussed.