  The interplay between spin and heat currents at magnetic
insulator|nonmagnetic metal interfaces has been a subject of much scrutiny
because of both fundamental physics and the promise for technological
applications. While ferrimagnetic and, more recently, antiferromagnetic systems
have been extensively investigated, a theory generalizing the heat-to-spin
interconversion in noncollinear magnets is still lacking. Here, we establish a
general framework for thermally-driven spin transport at the interface between
a noncollinear magnet and a normal metal. Modeling the interfacial coupling
between localized and itinerant magnetic moments via an exchange Hamiltonian,
we derive an expression for the spin current, driven by a temperature
difference, for an arbitrary noncollinear magnetic order. Our theory reproduces
previously obtained results for ferromagnetic and antiferromagnet systems.
