We present a formalism for an atomic scale study of phononic heat transfer. The expression of thermal energy current can be cast in the Landauer form and incorporates the transmission coefficient explicitly. Calculation of the thermal conductance of a monoatomic chain of N atoms between two reservoirs shows interesting quantum features. The conductance density appears as Lorentzian type resonances at the eigenfrequencies of the chain. At low-temperature limit the discrete vibrational frequency spectrum of a "soft" chain may reflect on the thermal conductance by giving rise to a sudden increase. At room temperature, the conductance through a "stiff" chain may oscillate with the number of chain atoms. The obtained quantum features are compared with similar effects found in the quantized electrical conductance.