How can half a degree of average temperature result in such devastating impact on coral reefs?
Coral die because of coral bleaching, a process in which the symbiotic algae living in the coral (which give the coral its colour), leave the coral host.

Bleaching can occur for a variety of reasons, but the ones that relate to a warming climate are:


Ocean acidification caused by dissolution of carbon dioxide in the water.
Thermal stress. According to this website, "Corals do best when ocean water is between 73 degrees F and 84 degrees F." (22–29 °C). Long durations of heated sea surface water exceeding that would cause bleaching and coral death. For example, a recent bleaching event in the Great Barrier Reef had temperatures of 4 °C above average, where the average is around 27 to 28. This puts it above the comfort zone of the coral.