thermodynamics, and state of matter transitions.

it requires energy to turn water into gaseous water. gaseous water moves to cooler places, will condense there, and will release the energy that was needed to turn it into a gas at that location. its the most natural mechanism of heat transfer. water evaporates where its warmer, and condenses where its cooler, energy is being moved around. your egg box is destined to strive for thermodynamic equilibrium. the laws of nature allow no alternative.

i see no issue. you heat it from below, how else is the heat going to distribute. with your setup, not only is it to be expected, it is mandated by the laws of nature.

the question is: will the ocassional drop of distilled water on the eggs harm the eggs? (condensed water dripping from a clean surface is pure). i say no. but here we can discuss. apart from that, whats going on here is not just natural, its inevitable with this setup. thermodynamics my friend, thermodynamics.