  We investigate numerically the magnetisation dynamics of an array of
nano-disks interacting through the magneto-dipolar coupling. In the presence of
a temperature gradient, the chain reaches a non-equilibrium steady state where
energy and magnetisation currents propagate. This effect can be described as
the flow of energy and particle currents in an off-equilibrium discrete
nonlinear Schr\"odinger (DNLS) equation. This model makes transparent the
transport properties of the system and allows for a precise definition of
temperature and chemical potential for a precessing spin. The present study
proposes a novel setup for the spin-Seebeck effect, and shows that its
qualitative features can be captured by a general oscillator-chain model
