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Thermal transport in nanostructures has attracted increasing attention in recent years,and many interesting physical effects such as the universal quantized thermal conductance1–4,thermal rectification effects5–7,and negative differential thermal resistance8,9 have been found in these systems.Here,we introduce our recent works on the thermal properties of nanowires,graphene nanoribbons and quantum structures:(1)We investigated the heat flux distribution in InAs/GaAs core-shell nanowires and demonstrate that core-shell nanowire is a promising structure as nanoscale heat cables.10(2)A study on thermal transport in quantum structures shows that the cutoff frequency for the lowest four types of acoustic modes is zero while the cutoff frequency for optical modes is nonzero.Quantized thermal-conductance plateau which can be observed in a perfect quantum wire is broken in the structure with catenoidal contacts.11(3)Phonon transport and thermal conductance show the similar thermal conductance property using nonequilibrium Greens function method and elastic wave continuum model at low temperatures.However,in the higher temperature region,the thermal conductance in nonequilibrium Greens function method is bigger than that in the elastic wave continuum model.12(4)We studied the thermal transport properties of graphene nanoribbons with pentagon–heptagon defect(PHD)by using first principles calculations in combination with non-equilibrium Greens function approach.The results show that the PHD effect on thermal conduction in armchair-oriented GNR is stronger than that in zigzag-oriented GNR.The out-of-plane acoustic mode is almost reflected by the PHD at a particular frequency.When the temperature is larger than 400 K,the thermal conduction ratio is only related to the PHDs orientation.