Fullerenes and cubane (C8H8) can be arranged to form heteromolecular crystals that exhibit interesting crystal phases. Experimental measurements indicate a rotor-stator phase for C60-cubane crystals in which the C60 molecules rotate freely whereas cubane molecules are essentially static. A similar phase is found for C70-cubane crystals but, due to C70’s asymmetry, hindered rotations can be observed in specific crystal phases. Details of the rotational dynamics of the fullerenes in these heteromolecular crystals are difficult to be completely assessed by experiments. To this end, we have performed classical molecular dynamics simulations of C70-cubane crystals to investigate the behavior of C70 fullerenes and cubanes in the face-centered cubic and body-centered tetragonal crystallographic phases. Our simulations show that, in the cubic phase, C70 molecules are allowed to freely rotate whereas cubanes act as molecular bearings. In the tetragonal phase, the cubane molecules also remain practically fixed and the rotation of C70 fullerenes becomes hindered. In this phase, C70 molecules rotate around the fivefold axis, which in turn precesses about the c crystallographic direction of the unit cell. Details regarding the dynamics (e.g., energy barriers, reorientational relaxation processes, and phonon-libration coupling) of the C70 molecules in both crystal phases are discussed. In general, our results agree with previous experimental findings for C70-cubane crystals.