  Thermal transport is less appreciated in probing quantum materials in
comparison to electrical transport. This article aims to show the pivotal role
that thermal transport may play in understanding quantum materials: the
longitudinal thermal transport reflects the itinerant quasiparticles even in an
electrical insulating phase, while the transverse thermal transport such as
thermal Hall and Nernst effect are tightly linked to nontrivial topology. We
discuss three types of examples: quantum spin liquids where thermal transport
identifies its existence, superconductors where thermal transport reveals the
superconducting gap structure, and topological Weyl semimetals where anomalous
Nernst effect is a consequence of nontrivial Berry curvature. We conclude with
an outlook of the unique insights thermal transport may offer to probe a much
broader category of quantum phenomena.
