# Will an egg hard boil faster at higher heat?

The water in a pot of water will boil at $$100°\text{C}$$ regardless of how much heat is applied to it after it begins to boil. The higher the heat, the faster the water boils off (but at $$100°\text{C}$$). The water is getting more thermal energy and dissipates into steam more quickly. Will a fully immersed egg hard boil faster, similarly absorbing more cooking heat energy per second at high heat vs. a low boil? Or, is the hard boiling time only affected by the temperature of the water the egg is immersed in?