  We study the role of thermal magnons in the spin and heat transport across a
normal-metal/insulating-ferromagnet interface, which is beyond an elastic
electronic spin transfer. Using an interfacial exchange Hamiltonian, which
couples spins of itinerant and localized orbitals, we calculate spin and energy
currents for an arbitrary interfacial temperature difference and misalignment
of spin accumulation in the normal metal relative to the ferromagnetic order.
The magnonic contribution to spin current leads to a temperature-dependent
torque on the magnetic order parameter; reciprocally, the coherent precession
of the magnetization pumps spin current into the normal metal, the magnitude of
which is affected by the presence of thermal magnons.
