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Heat can be transferred from hot to cold areas by various carriers. In particular, heat conduction is mediated by vibrations and electrons, and thermal radiation by photons. This chapter recapitulates various ways to account for the modification of the heat carrier properties at the nanoscale, when either Fourier's law of heat diffusion is not valid or macroscopic incoherent thermal radiation cannot be applied. The main part of the chapter deals with heat conduction. Limitations of the heat equation are enumerated and heat carrier properties in crystalline, amorphous and polymeric materials are described. Thermal boundary resistances, confinement in thin films and nanowires, thermal constrictions and sub-mean free path sources are addressed. Then, near-field thermal radiation is introduced. All these effects can come into play in the thermal nanometrology experiments that are briefly presented at the end.

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