Yes, warm temps can make them hatch sooner, but that is usually only a problem when they are in an incubator, as its easier to make a mistake with the temp. Since the eggs are under her, I doubt that would be a problem.
Could have been a rat/snake etc, although I would think they would have eaten most of the contents, maybe the two broodies were fighting over eggs and the egg rolled out of the nest and broke, or a chicken/duck starting pecking at it.
It may be due to lack of turning of the egg, some broodies aren't as diligent as other's. I've seen that with a few of my eggs, and they have all hatched.