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Incorporation of radiant boundary conditions is proposed for multiphysics (electromagnetic and thermal) modeling to cover practically valuable scenarios of hybrid (heat radiation and microwave) thermal processing of materials. The algorithm is implemented by making the models of radiation in ANSYS Fluent available for the electromagnetic models in QuickWave-3D. The resulting simulator is applied to the process of hybrid heating of cylindrical samples of limestone in Ceralink's MATTM kiln. Time-temperature history of the heating process is simulated along with the temperature field. Hybrid heating is shown to be more efficient in terms of heating rate and tempera-ture uniformity.