Building upon prior experience, we intend to conduct a theoretical investigation in three aspects concerning the critical thermal conduction process that limits the efficient heat dissipation for the next-generation phase-change memory devices, namely, the thermal conduction conversion mechanism during crystalline-to-amorphous transition, low-dimensional heat conduction, and interface thermal resistance. The aim is to clarify the competing mechanisms among different phonon scattering processes induced by decreased spatial dimensions, structural ordering, and phonon harmonicity and to establish a computational framework bridging microscale phonon behavior and macroscopic heat conduction. Ultimately, this endeavor seeks to provide quantitative theoretical foundations for thermal transport and management in the practical application of phase-change memory devices.