While the spin Seebeck effect (SSE) has proven to be an invaluable tool for probing spin cor- relations in collinear magnetic insulators, a theory generalizing the heat-to-spin interconversion in noncollinear magnets is still lacking. Nonetheless, a variety of quantum magnets that are attracting an increasing attention to, e.g., their topological properties, display a noncollinear spin order. 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 cur- rent, driven by a temperature difference, for an arbitrary noncollinear magnetic order. Our theory reproduces previously obtained results for ferromagnetic and antiferromagnet systems.