Coral reef systems are under increasing pressure to adapt to rapidly varying environmental conditions, in particular increasing ocean temperatures. A question of major concern is whether coral reefs can adapt to and survive the predicted increases in global temperatures over the remainder of this century. A simple model of a coral reef ecosystem is developed to include adaptation of key growth and mortality parameters for a coral polyp population and its symbiotic algae population. Interacting populations of pelagic phytoplankton and zooplankton are also simulated. The model simulates a stable coral reef ecosystem in the absence of climate change, but predicts the extinction of the coral population under global warming if the populations do not adapt. However, when the coral and symbiont populations adapt to climate change, a stable coral reef ecosystem is predicted. The model allows identification of processes and parameters to inform attempts to measure the key attributes of adapting coral reef ecosystems.