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In the framework of Greens function theory out of equilibrium, a Landauer-Buttiker (LB) formula for thermal conductance is derived. A simplified model for describing extremely cold dielectric chains is proposed for the first time. Fhrther we apply the present LB formula for studying thermal conductance at low-lying modes, emerging in dielectric atom chains. We find that quantum thermal conductance undergoes an anomalous transition due to new quasiparticle excitations, resulting from nonlinear atom-atom interactions. This theoretical prediction is in excellent agreement with a high-accuracy measurement to thermal conductance quantum.