The immersed boundary method (IBM) is gaining attention in the computational fluid dynamics but its applications in the field of a conjugated radiative–conductive or radiative–convective heat transfer seem limited. Therefore, the paper presents extension of this method to heat transfer problems dominated by thermal radiation in a nongray medium. The present model enables simulation of heat and fluid flows in a domain with complex stationary or moving internal and external boundaries on a fixed Cartesian grid (FCG) by applying the finite volume method. The special attention is paid to modeling thermal radiation and optical phenomena at highly curved, opaque, or transparent boundaries which confine the computational domain or separate zones of different thermophysical and optical properties, e.g., different values of a refractive index. The model is limited to a 2D planar or axisymmetric spaces. Detailed verification procedure proves accuracy and correctness of the developed model and shows its potential application field. The model may be used for simulations of a conjugated radiative–conductive or radiative–convective heat transfer in a nongray medium in a complex domain with opaque or transparent curved internal or external boundaries without unstructured or body fitted mesh generation.