The full Brinkman equation coupled with the heat and mass transfer equations was solved numerically using the finite element technique. A square cavity filled with hydrocarbon nanofluid of fullerene–toluene with different concentration values of fullerene was subject to various heating conditions. Results have confirmed that in the presence of nanofluid a heat transfer enhancement is present until a certain amount of initial concentration of the nanofluids. The heat convection coefficient was found to be 16% higher when nanofluid is used as the wetting fluid. In addition, it was determined that the concentration of fullerene in toluene has its limitation in heat removal enhancement. In fact, beyond 5% of fullerene, there is no noticeable enhancement of the heat removal in the system. The model was also used to study thermodiffusion effects in the cavity. Despite the small value and negligible effects of thermodiffusion in general heat and mass transfer problems, which is <5% in the case of studying nanofluids, a maximum value of 20% variation of fullerene concentration has been detected. Moreover, fullerene separation was investigated for different heating intensities. As the Rayleigh number increases, the mixing was found to reduce the separation, which diminishes the Soret effect in the system.