The magnetic insulator yttrium iron garnet can be grown with near perfection and is therefore and ideal conduit for spin currents. It is a complex material with 20 magnetic moments in the unit cell. In spite of being a ferrimagnet, YIG is almost always modeled as a simple ferromagnet with a single spin wave mode. We use the method of atomistic spin dynamics to study the temperature evolution of the full spin wave spectrum, in quantitative agreement with neutron scattering experiments. The antiferromagnetic or optical mode is found to suppress the spin Seebeck effect at room temperature and beyond due to thermally pumped spin currents with opposite polarization to the ferromagnetic mode.