Actually, there is a real danger to coral reefs, but it's mostly from the murky water caused by agricultural runoff. Water temperatures a few degrees higher won't kill coral - it actually makes a lot of species really flourish.
Untreated sewage directly discharged into the coastal waters is also a problem, especially for many tropical countries (i.e., Third World) where the reefs occur offshore. Growing urban coastal populations exacerbate this problem.