This paper studies one of the magnetic analogs of well-known thermoelectric effects, the spin Thomson effect. This effect consists in the existence of a heat flux caused by the spin current and is described by a modified heat equation. When comparing the published experimental data and the theoretical model, it was possible to find the Thomson spin coefficient for iron-yttrium garnet. From a viewpoint of thermal conductivity, the presence of a magnetic field of 1750 Oe turns out to be equivalent to the motion of the medium at a rate of 6.5 mm/s and leads to the existence of a giant heat flux of 18.9 kW/m2 due to the transfer of heat by spins. The ability to control heat fluxes by means of a magnetic field allows the use of materials based on iron-yttrium garnet for practical applications as thermal switches for solid-state cooling.