  Despite governing heat management in any realistic device, the microscopic
mechanisms of heat transport in all-solid-state electrolytes are poorly known:
existing calculations, all based on simplistic semi-empirical models, are
unreliable for superionic conductors and largely overestimate their thermal
conductivity. In this work, we deploy a combination of state-of-the-art methods
to calculate the thermal conductivity of a prototypical Li-ion conductor, the
Li$_3$ClO antiperovskite. By leveraging ab initio, machine-learning, and
force-field descriptions of inter-atomic forces, we are able to reveal the
massive role of anharmonic interactions and diffusive defects on the thermal
conductivity and its temperature dependence, and to eventually embed their
effects into a simple rationale which is likely applicable to a wide class of
ionic conductors.
