Inorganic clathrates such as Ba8GaxGe46−x and Ba8AlxSi46−x commonly exhibit very low thermal conductivities. A quantitative computational description of this important property has proven difficult, in part due to the large unit cell, the role of disorder, and the fact that both electronic carriers and phonons contribute to transport. Here, we conduct a systematic analysis of the temperature and composition dependence of low-frequency modes associated with guest species in Ba8GaxGe46−x and Ba8AlxSi46−x (“rattler modes”), as well as of thermal transport in stoichiometric Ba8Ga16Ge30. To this end, we account for phonon-phonon interactions by means of temperature-dependent effective interatomic force constants, which we find to be crucial in order to achieve an accurate description of the lattice part of the thermal conductivity. While the analysis of the thermal conductivity is often largely focused on the rattler modes, here it is shown that at room temperatures modes with ħω≥10 meV account for 50% of lattice heat transport. Finally, the electronic contribution to the thermal conductivity is computed, which shows the Wiedemann-Franz law to be only approximately fulfilled. As a result, it is crucial to employ the correct prefactor when separating electronic and lattice contributions for experimental data.