Two-dimensional metal–organic frameworks (2D MOFs) offer tunable interlayer coupling and low lattice stiffness, making them a compelling system for exploring stacking-dependent heat transport. In this work, we present a full ab initio investigation of lattice dynamics and thermal transport in copper benzenehexathiolate ( \(\mathrm{Cu_3BHT}\) ), focusing on three distinct stacking arrangements: AA, AB, and C. Our phonon calculations show that AB is dynamically unstable, whereas the C phase is the thermodynamic ground state, lower in energy than AA by \(\sim 18\) meV per formula unit, and features covalent Cu–S interlayer bonds that stiffen interlayer modes and enhance through-plane transport. Using Boltzmann transport (BTE-RTA) together with the Wigner formalism, we find that coherent phonon contributions are essential to capture the temperature dependence: they significantly raise \(\kappa\) and reduce the classical \(T^{-1}\) scaling to \(\kappa \propto T^{-\alpha }\) with \(\alpha <1\) in both AA and C configurations, evidencing a wave-like transport channel activated by near-degenerate, hybridized modes. These results identify stacking-controlled interlayer connectivity as a design lever for directional heat management in 2D MOFs, with potential implications where low lattice thermal conductivity is desirable.
