"Computations show that a material made with just the right amounts of hafnium, nitrogen, and carbon would have a melting point of more than 4400 K (7460°F). That's about two-thirds the temperature at the surface of the sun and 200 K higher than the highest melting point ever recorded experimentally."
"The work shows that Hf-Ta-C combined a high heat of fusion (the energy released or absorbed when it transitions from solid to liquid) with a small difference between the entropies (disorder) of the solid and liquid phases. "What makes something melt is the entropy gained in the process of phase transformation," van de Walle explains. "So if the entropy of the solid is already very high, that tends to stabilize the solid and increase the melting point."
Researchers then used those findings to look for compounds that might maximize those properties. They found that a compound with hafnium, nitrogen, and carbon would have a similarly high heat of fusion but a smaller difference between the entropies of the solid and the liquid. When they calculated the melting point using their computational approach, it came out 200 K higher than the experimental record."
This suggests that the material with the highest melting point would have a very high entropy, so that the energy released when transitioning to a liquid is low. That would also possibly suggest that that material would be not a particularly useful "solid" - as it would already be as close to "liquid" as possible.