We investigate the heat transport mechanisms responsible in driving the characteristic temperature-dependent thermal conductivities of C60 and PCBM crystals via molecular dynamics simulations. We find that the thermal conductivity of PCBM is "ultralow" across the temperature range studied in this work. In contrast, the temperature-dependent thermal conductivity of C60 crystals exhibits two regimes: "crystal-like" behavior at low temperatures where thermal conductivity increases rapidly with decreasing temperature and temperature-independent thermal conductivities at higher temperatures. The spectral contributions to thermal conductivity for C60 suggest that the majority of heat is carried by modes in the low-frequency regime (<2 THz), which is a consequence of intermolecular interactions. Unlike for C60, these modes are not responsible for heat conduction in PCBM due to the mismatch in density of states introduced by the addition of low-frequency modes from the alkyl chains that are attached to the fullerene moieties.