The interfacial thermal resistance (ITR) between a carbon nanotube (CNT) and adjoining carbon, silicon, or copper substrate is investigated through non-equilibrium molecular dynamics simulation (NEMD). The theoretical phonon transmission also is calculated using a simplified form of the diffuse mismatch model (DMM) with direct simulation of the phonon density of states (DOS) under quasi-harmonic approximation. The results of theory and simulation are reported as a function of temperature in order to estimate the importance of anharmonicity and inelastic scattering. At 300K, the thermal conductance of CNT-substrate interfaces is ∼1500 W/mm2K for diamond carbon, ∼500 W/mm2K for silicon, and ∼250 W/mm2K for copper.