Extensive equilibrium molecular dynamics (MD) simulations have been performed to investigate thermal conduction mechanisms via the Green-Kubo approach for (type II) hydrogen hydrate, at 0.05 kbar and between 30 and 250 K, for both lightly-filled H 2 hydrates (1s4l) and for more densely-filled H 2 systems (2s4l), in which four H 2 molecules are present in the large cavities, with respective single-and doubleoccupation of the small cages. The TIP4P water model was used in conjunction with a fully atomistic hydrogen potential along with long-range Ewald electrostatics. It was found that substantially less damping in guest-host energy transfer is present in hydrogen hydrate as is observed in common type I clathrates (e.g., methane hydrate), but more akin in to previous results for type II and H methane hydrate polymorphs.This gives rise to larger thermal conductivities relative to common type I hydrates, and also larger than type II and H methane hydrate polymorphs, and a more crystallike temperature dependence of the thermal conductivity. a) Corresponding author.