I lived in Mexico where it was very hot as well. We didn't even have a refrigerator and I don't every remember an egg rotting. Perhaps you could at least check them to make sure they're good. I believe they will be fine.
I have a hen who crows constantly. I've tried putting a standard milk crate over her at night so that she can't extend to crow and I also cover her with a tarp so that she can't see what time of day or night it is. She still crows. Any suggestions on how to get her to stop, short of...