We investigate the thermalization of charm quarks in high energy heavy ion collisions. To this end, we calculate the diffusion coefficient in the perturbative Quark Gluon Plasma and relate it to collisional energy loss and momentum broadening. We then use these transport properties to formulate a Langevin model for the evolution of the quark spectrum in the hot medium. We solve the Langevin equations numerically in a hydrodynamic simulation of the heavy ion reaction. The results of this simulation are the medium modifications of the charm and bottom spectrum and the expected elliptic flow $v_2(p_T)$ as a function of the diffusion coefficient. These results are compared to experiment. The diffusion coefficient can be constrained by lattice QCD calculations.