Carbon nanotube bundles are promising thermal interfacial materials due to their excellent thermal and mechanical characteristics. In this study, the phonon dispersion relations and density of states of the single-wall carbon nanotube bundles are calculated by using the force constant model. The calculation results show that the inter-tube interaction leads to a significant frequency raise of the low frequency modes. To verify the applied calculation method, the specific heat of a single single-wall carbon nanotube is calculated first based on the obtained phonon dispersion relations and the results coincide well with the experimental data. Moreover, the specific heat of the bundles is calculated and exhibits a slight reduction at low temperatures in comparison with that of the single tube. The thermal conductivity of the bundles at low temperatures is calculated by using the ballistic transport model. The calculation results indicate that the inter-tube interaction, i.e. van der Waals interaction, hinders heat transfer and cannot be neglected at extremely low temperatures. For （5, 5） bundles, the relative difference of the thermal conductivity caused by ignoring inter-tube effect reaches the maximum value of 26% around 17 K, which indicates the significant inter-tube interaction effect on the thermal conductivity at low temperatures.
