It has been proposed that corals with symbiotic algae (Symbiodinium) bleach under thermal stress due to temperature‐dependent inactivation of the Rubisco protein that impairs CO2 uptake, causing a backlog of electrons that result in the formation of damaging Reactive Oxygen Species. We present a numerical model of this mechanism of photoinhibition for symbiotic algae residing within coral tissue. The resulting rate of bleaching depended on temperature, light intensity, and the rate of heterotrophic feeding. The model was validated using three independently published experimental data sets. The model was capable of capturing both the diurnal change in the state of the photosystem, as well as changes in the symbiont population and the coral host caused by different temperature, light, and feeding treatments. Elevated temperatures and light led to a degradation of the photosystem and the expulsion of symbiont cells. If the coral fed heterotrophically, this degradation of the photosynthetic apparatus was reduced, but still a clear decrease in maximum quantum yield (Fv : Fm) and cell numbers was observed when the coral was exposed to elevated temperature. The reduction in chlorophyll content of cells at elevated temperatures and light was compared with the observational bleaching index Degree Heating Days (DHD). As quantified by DHD, the model was found to bleach under similar thermal stress regimes as field studies, except under elevated heterotrophic feeding conditions, which resulted in reduced severity of bleaching over a 90 d period.