Scrutinizing distinct solid/liquid (s/l) and solid/solid (s/s) phase transitions (passive transitions) for large change in bulk (and homogenous) thermal conductivity, we find the s/l semiconductor/metal (S/M) transition produces largest dimensionless thermal conductivity switch (TCS) figure of merit Z TCS (change in thermal conductivity divided by smaller conductivity). At melting temperature, the solid phonon and liquid molecular thermal conductivities are comparable and generally small, so the TCS requires localized electron solid and delocalized electron liquid states.For cyclic phase reversibility, the congruent phase transition (no change in composition) is as important as the thermal transport. We identify XSb and XAs (X = Al, Cd, Ga, In, Zn) and describe atomic-structural metrics for large Z TCS , then show the superiority of S/M phonon-to electrondominated transport melting transition. We use existing experimental results and theoretical and ab initio calculations of the related properties for both phases (including the Kubo-Greenwood and Bridgman formulations of liquid conductivities). The 5p orbital of Sb contributes to the semiconductor behavior in the solid-phase bandgap and upon disorder and bond-length changes in the liquid phase this changes to metallic, creating the large contrast in thermal conductivity.The charge density distribution, electronic localization function, and electron density of states are used to mark this S/M transition. For optimal TCS, we examine the elemental selection from the transition-, basic-and semimetals and semiconductor groups. For CdSb, addition of residual Ag suppresses the bipolar conductivity and its Z TCS is over 7, and for Zn 3 Sb 2 it is expected to be over 14, based on the structure and transport properties of the better known β-Zn 4 Sb 3 . This is the highest Z TCS identified. In addition to the metallic melting, the high Z TCS is due to the electron-poor nature of II-V semiconductors leading to the significantly low phonon conductivity.