Corals produce polyps that are mobile early in life and wash all over. They won't have any trouble moving if temperatures change. In fact it's already been observed to happen.
https://www.nature.com/news/2011/110121/full/news.2011.33.ht...
Corals are not going to die out in 30 years, 50 years, probably not before humans die out. Corals have been around for a long time and are highly adaptable.
https://en.wikipedia.org/wiki/Fossil_Coral_Reef
For fun you can look at temps and C02 levels during Devonian period. No glaciers, much warmer than today. Very high C02 because carbon we are burning today had not been sequestered yet. Yet a coral reef was formed, a big one.