While quasilocalized vibrational modes (QVMs) in glassy solids are known to populate the low-frequency spectrum, their thermal transport properties remain largely unexplored. It is known that the energy of localized vibrational modes spatially remains where they reside. QVMs are therefore hypothesized to be inefficient heat carriers. We here show that the modal thermal conductivity of QVMs is at the same magnitude as that of the delocalized vibrational modes, which demonstrates QVMs can be efficient heat carriers as delocalized vibrational modes. We further prove that the mutual coherence between QVMs and other modes explains their high thermal exchange performance. Our finding provides a perspective on the thermal transport behavior of QVMs in glassy solids.