There is growing evidence that different coral species and algal symbionts (Symbiodinium spp.) can vary greatly in their response to rising temperatures and also ocean acidification. In a fully crossed factorial experimental design, two threatened Caribbean reef-building coral species, Acropora cervicornis hosting a mixture of Symbiodinium clades A and C and Orbicella faveolata hosting Symbiodinium D, were exposed to combinations of a normal (26°C) and elevated (32°C) temperature and normal (380 ppm) and elevated (800 ppm) CO2 for 62 d and then recovered at 26°C and 380 ppm or 32°C and 380 ppm for an additional 56 d. CO2 enrichment did not confer enhanced thermal tolerance as had been suggested in other studies. A. cervicornis was more sensitive to heat stress (maximum monthly mean + 1.5°C) experiencing 100% mortality after 25 d while all O. faveolata survived. Conversely, O. faveolata was more sensitive to high CO2 experiencing a 47% reduction in growth while A. cervicornis experienced no significant reduction. It is predicted that A. cervicornis is unlikely to survive past 2035. O. faveolata with D symbionts might survive to 2060 and later but its abundance will be impacted by CO2 effects on recruitment potential.