Creating, manipulating and detecting spin polarized carriers are the key elements of spin based electronics. Most practical devices use a perpendicular geometry in which the spin currents, describing the transport of spin angular momentum, are accompanied by charge currents. In recent years, new sources of pure spin currents, i.e., without charge currents, have been demonstrated and applied. In this paper, we demonstrate a conceptually new source of pure spin current driven by the flow of heat across a ferromagnetic/non-magnetic metal (FM/NM) interface. This spin current is generated because the Seebeck coefficient, which describes the generation of a voltage as a result of a temperature gradient, is spin dependent in a ferromagnet. For a detailed study of this new source of spins, it is measured in a non-local lateral geometry. We developed a 3D model that describes the heat, charge and spin transport in this geometry which allows us to quantify this process. We obtain a spin Seebeck coefficient for Permalloy of -3.8 microvolt/Kelvin demonstrating that thermally driven spin injection is a feasible alternative for electrical spin injection in, for example, spin transfer torque experiments.