Will mirrors mounted over a brick fireplace crack from the heat?

They should not. The masonry chimney in our house becomes only warm to the touch after a few days of a continuous burn, and most mirrors will be mounted so that there is a least a small airspace between the mirror and the chimney. If a mirror were to be firmly attached to a chimney at multiple places, it COULD crack from the minor expansion of the brick- but a framed mirror HUNG from a chimney should not. Most of the pre-civil war estate house in Virginia have mirrors above the mantels- with no cracks.