  The propagation of magnons in temperature gradients is investigated within
the framework of an atomistic spin model with the stochastic
Landau-Lifshitz-Gilbert equation as underlying equation of motion. We analyze
the magnon accumulation, the magnon temperature profile as well as the
propagation length of the excited magnons. The frequency distribution of the
generated magnons is investigated in order to derive an expression for the
influence of the anisotropy and the damping parameter on the magnon propagation
length. For soft ferromagnetic insulators with low damping a propagation length
in the range of some $\mu$m can be expected for exchange driven magnons.
