Certain elements and composites in the real world have significant melting and boiling points. The metal with the highest values is tungsten, with 3,695 K and 6,203 K, respectively. According to our friends over in Chemistry, carbon has an even higher melting point of 3,823 K, while even more resilient materials exist, such as tantalum hafnium carbide (4,263 K) or the potential new record-holder HfN0.38C0.51 (4,400 K).
Chemistry was also kind enough to discuss what gives materials such high phase-change temperatures, but my understanding of chemistry isn't sufficient to expand on the information I've found so far (or, to be honest, grok the information over on Chemistry).
Using only what we currently know and can theorize, what's the highest melting and boiling points we can give an element or compound?
My goal for this is to have a material that functions as a molten ooze at 10,255 K and normal air pressure at Earth sea level, and doesn't produce toxic fumes.