Flat-band systems, characterized by dispersionless energy bands and compact localized states, have emerged as promising platforms for exploring strongly correlated phenomena in condensed-matter physics. While extensively studied in electronic systems, their potential in nanophotonics and thermal management remains underexplored. In this work, we investigate the flat-band phenomena in quasi-one-dimensional stub lattices composed of silicon carbide nanoparticles on the basis of many-body radiative heat transfer. Employing the dipole approximation, we account for long- and short-range interactions to compute band structures under periodic and open boundary conditions, revealing dispersionless flat bands and compact localized states characterized by high inverse participation ratios and sublattice-selective dipole distributions due to geometrical frustration. Boundary conditions significantly modulate radiative heat transfer between chain ends, exhibiting distinct spectral peaks and $l^{-2}$ scaling in long chains up to 500 unit cells. Furthermore, temporal dynamics is analyzed via eigenmode decomposition of the linearized response matrix, showing that the stub geometry suppresses the spatial spreading of local thermal perturbations and confines the temperature response more strongly than the one-dimensional periodic chain. These findings provide insight into how flat-band-inspired geometry shapes near-field radiative heat transport and offer a route to boundary-controlled nanophotonic thermal management.

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• Flat bands
• Fluctuation-dissipation theorem
• Heat radiation
• Phonon polariton
• Dipole approximation
• Green's function methods