Thermal conductivity of any material is dependent on two things: i)The motion of free electrons ii) Lattice vibrations Thermal conductivity of liquids decreases with increasing temperature as the liquid expands and the molecular move apart. In the case of solids because of lattice distortings higher temperatures make it difficult for electrons to flow, hence the thermal conductivity of metals decreases at non-metals, electronic conductivity is practically non-existent and due to an increase in phonon conduction, the thermal conductivity increases.