The development of materials that reversibly store high densities of thermal energy is critical to the more efficient and sustainable utilization of energy. Herein, we investigate metal-organic compounds as a new class of solid-liquid phase-change materials (PCMs) for thermal energy storage. Specifically, we show that isostructural series of divalent metal amide complexes featuring extended hydrogen bond networks can undergo tunable, high-enthalpy melting transitions over a wide temperature range. Moreover, these coordination compounds provide a powerful platform to explore the specific factors that contribute to the energy density and entropy of metal-organic PCMs. Through a systematic analysis of the structural and thermochemical properties of these compounds, we investigated the influence of coordination bonds, hydrogen-bond networks, neutral organic ligands, and outer-sphere anions on their phase-change thermodynamics. In particular, we identify the importance of high densities of coordination bonds and hydrogen bonds to achieving a high PCM energy density, and we show how metal-dependent changes to the local coordination environment during melting impact the entropy and enthalpy of metal-organic PCMs. These results highlight the potential of manipulating order-disorder phase transitions in metal-organic materials for thermal energy storage.