I introduce a mode-resolved quantum Langevin method that tracks coherent phonon heat transport at any temperature from a single eigendecomposition of the dynamical matrix. The result is a closed-form, multiterminal conductance $G_{\alpha \beta }\left(T\right)$. I derive the expressions and provide an analytical connection to nonequilibrium Green's functions (NEGF), recovering the Landauer–Büttiker limit under weak, diagonal damping. Benchmarks on a harmonic chain reproduce the canonical $\kappa \propto T$ law. A vacancy-defected carbon nanotube shows quantitative agreement with NEGF transmission spectra. I then apply the method to proteins viewed as multiterminal elastic networks, where surface patches and solvent interfaces serve as contacts. The framework yields the full $G_{\alpha \beta }\left(T\right)$ and a mode-level diagnostic linking conductance, frequency, and localization. The ensuing spectral weights reveal a mobility edge via a temperature crossover $T_c\simeq \hslash {\omega }_c/k_B$. The approach yields fast, interpretable predictions for complex phonon systems from a single eigensolve.

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• Ballistic transport
• Bosons
• Fluctuation-dissipation theorem
• Heat transfer
• Localization
• Nonequilibrium statistical mechanics
• Percolation
• Phonons
• Quantum transport
• Thermal boundary conductance
• Thermal properties
• Transport in networks