We present the results of classical molecular dynamics simulations to assess the relative contributions to interfacial thermal conductance from inelastic phonon processes at the interface and in the adjacent bulk materials. The simulated system is the prototypical interface between argon and “heavy argon” crystals, which enables comparison with many past computational studies. We run simulations interchanging the Lennard-Jones potential with its harmonic approximation to test the effect of anharmonicity on conductance. The results confirm that the presence of anharmonicity is correlated with increasing thermal conductance with temperature, which supports conclusions from prior experimental and theoretical work. However, in the model Ar/heavy-Ar system, anharmonic effects at the interface itself contribute a surprisingly small part of the total thermal conductance. The larger fraction of the thermal conductance at high temperatures arises from anharmonic effects away from the interface. These observations are supported by comparisons of the spectral energy density, which suggest that bulk anharmonic processes increase the interfacial conductance by thermalizing energy from modes with low transmission to modes with high transmission.