For clarification I’m asking about unfertilized chicken eggs. This in reference to a recent Ars Technica where AI is copying a (conventionally incorrect) YES
Obviously when you first apply heat, the egg will solidify, but if one keeps going, will the egg eventually melt? I mean it will eventually vaporize, but I’m not sure it will melt.
Brian
Egg whites are formed of protein chains that naturally coil up into microscopic balls that slide over each other, forming a liquid substance.
Heating the egg causes the protein chains to unfold, a process called “denaturing”. The proteins unfold and become long chains, which means they no longer flow. This is the solidification of the egg.
If you keep heating the egg, the chemicals forming the protein chains will eventually combust through chemical reactions with the oxygen in the air.
Theoretically you could probably keep the egg in a vacuum to prevent combustion. If you did this, all the water mollecules in the egg would evaporate away as you heat up the egg, as will other impurities; eventually you’ll just be left with the carbon chains that form the egg (and calcium if you left the shell).
The shell will melt at 1,548 degrees while the carbon won’t melt until 3,550, so if you can keep the egg in a vacuum chamber while heating it up to 3,600 degrees or so, you may have a chance?
It’s pointed out that one can melt an (uncooked) egg by freezing it first…
Brian
in the “best kind of correct” way
Presumably even without a vacuum you could burn the egg and then melt the ashes.
Oh, yummy! 
well done
Eggs over Dali.
No, very rare.
Some eggs are made of chocolate and melt more easily. Others require tremendous amounts of heat to turn proteins into amino acids into something not solid.
So this got me wondering about egg yolks, compared to cheese. Googling gets me these figures -
Egg yolk 50% water 37% fat, 17% protein
Hard cheese 37% water 33% fat, 23% protein
So they are fairly similar in gross composition, but egg yolk doesn’t solidify into cheese-like texture even if you chill it. Presumably that’s by evolutionary design.
104% yolky goodness!
I think “melt” means converting the physical phase from solid to liquid, implying that the substance remains the same and it is only the phase that changes, not the chemistry.
Lots of substances won’t melt. They pyrolize, they change chemicals.
Everything reduces to isolated elements eventually, and those can all melt (if they’re not already liquid or gas). But I don’t think that counts as the original thing melting.
So, my vote is “no”.