Given enough temperature, can't you melt an egg?
"In 2015, a team of chemists in the US and Australia showed they could reverse the process. They added urea to liquefy the boiled egg whites, then put them in a vortex device to pull apart the proteins and return them to their original state." https://www.sciencefocus.com/science/can-you-unboil-an-egg
Just guessing here. I’m no thermodynamics expert, just a guy who melt things occasionally.
That is ignoring any interaction with the shell, which should melt around 1600 K.