 Solution

In the cold solid, phonon scattering makes $\tau \propto T^{-1}$ and therefore conductivity falls as temperature rises, at roughly fixed carrier density. After melting and ionization, the character of scattering changes; a hot Coulomb plasma eventually follows an increasing $T^{3/2}$ branch. A minimum in the crossover region is natural, but a weakly coupled plasma formula is not quantitatively justified throughout the warm dense regime.