Temperature gradients can cause spin currents, which rest solely on spin waves (magnons) and are not based on any electron motion. Hence even in ferromagnetic insulators spatial temperature gradients can lead to a magnon accumulation resulting in the so-called spin Seebeck effect [1]. It has been shown recently, that the strength of the spin Seebeck effect depends on the thickness of the magnetic insulator [2]. These findings foster an increasing interest in understanding of magnonic transport, raising especially the question of its relevant length scales [3,4].