I assume you refer to heat conductivity? If not, what I say next about heat conductivity can also be applied to electric conductivity when employing the Wiedemann Franz law relating the two. 

Heat conductivity is proportional to the heat capacity. At low temperature, the T-dependence of the heat capacity (e.g. T^3 -dependence for the lattice contribution) determines the T-dependence of the heat conductivity. At higher temperatures, phonon scattering plays a role and the T-dependence of the heat conductivity is determined by the T-dependence of the mean free path. All of the above, the simple theory of heat conductivity and the Wiedemann Fanz law relating heat conductivity and electric conductivity, can be found e.g. in the solid state textbook of Kittel.