Does it have to be warm for the butterfly egg to hatch?

Yes, they do have to be kept warm, but not necessarily by a sitting mother. A nesting goose or duck will get up at least once a day to leave the nest for a swim, get something to eat or just a stretch. The time she spends away from the nest is not long and usually she covers the eggs with a layer of down to keep them warm.

In the case of Canada Geese, when the mother does leave the nest for a break, the father is often close by standing guard to stop any prediators from attacking the nest.