Thermal engineering of quantum devices has attracted much attention since the discovery of quantized thermal conductance of phonons. Although easily submerged in numerous excitations in macrosystems, quantum behaviors of phonons manifest in nanoscale low‐dimensional systems even at room temperature. Especially in nanotransport devices, phonons move quasiballistically when the transport length is smaller than their bulk mean free paths. It has been shown that the phonon nonequilibrium Green's function method (NEGF) is effective for the investigation of nanoscale quantum transport of phonons. Here, two aspects of thermal engineering of quantum devices are discussed using NEGF methods. One covers transport properties of pure phonons; the other concerns caloritronic effects, which manipulate other degrees of freedom, such as charge, spin, and valley, via the temperature gradient. For each part, the basic theoretical formalisms are outlined first, then a survey of related investigations on models or realistic materials is presented. Particular attention is given to phonon topologies and the generalized phonon NEGF method. Finally, conclusions are offered and the study is summarized with an outlook.