Kapitza resistance is the thermal boundary resistance encountered between a solid and helium in cryogenics. A cold helium heat bath can coexist with a warmer immersed component under continuous heating. The bath's temperature alone therefore does not establish the component's temperature. Kapitza thermal boundary experiment supplied an early direct demonstration of the obstacle at the solid–liquid boundary.
A microscopic route to interfacial heat transfer is transmission of phonons. Transmission depends on the two materials and their interface; scattering and the condition of the surface matter. [ref]
Thermal boundary resistance by E. T. Swartz and Robert Otto Pohl. Swartz and Pohl (1989), abstract: phonon transmission, scattering and surface sensitivity
The fourth-power thermal boundary model isolates one useful low-temperature limiting law without assigning an empirical coefficient to a particular sample. New to topics? Read the docs here!