When a magnetic field is applied in the perpendicular direction to a metallic disk under the action of a radial bias voltage, a tangential electric current superimposes to the radial current due to the presence of the Lorentz force which acts on electrons. Here we introduce a thermal analog of this Corbino effect in many-body systems made of nonreciprocal bodies which interact by exchanging photons in near-field regime. In systems out of thermal equilibrium with a radial temperature gradient, we demonstrate that the Poynting field in the Corbino geometry is bent in presence of an external magnetic field, giving rise to a tangential heat flux. This thermomagnetic effect could find applications in the field of thermal management and energy conversion at nanoscale.