The dependence of Spin Seebeck effect (SSE) with the thickness of the magnetic materials is studied by means of incoherent thermal excitation. The SSE voltage signal in Fe3O4/Pt bilayer structure increases with the magnetic material thickness up to 100 nm, approximately, showing signs of saturation for larger thickness. This dependence is well described in terms of a spin current pumped in the platinum film by the magnon accumulation in the magnetic material. The spin current is generated by a gradient of temperature in the system and detected by the Pt top contact by means of inverse spin Hall effect. Calculations in the frame of the linear response theory adjust with a high degree of accuracy the experimental data, giving a thermal length scale of the magnon accumulation (Λ) of 17 ± 3 nm at 300 K and Λ = 40 ± 10 nm at 70 K.