In temperate rocky reefs of the Mediterranean, the corals Cladocora caespitosa and Astroides calycularis live at sites with ambient seawater pH and at adjacent submarine volcanic CO2 vent sites with low seawater pH where it is more energetically demanding to grow. We collected corals from distinct ambient pH (average pHT 8.05) and lower pH CO2 vent sites (average pHT 7.74–7.90) and quantified their physiological health and heterotrophic capacity (i.e., feeding capacity). This dataset is included in the OA-ICC data compilation maintained in the framework of the IAEA Ocean Acidification International Coordination Centre (see https://oa-icc.ipsl.fr). Original data were extracted from tables in the related paper (see Related to) by the OA-ICC data curator. In order to allow full comparability with other ocean acidification data sets, the R package seacarb (Gattuso et al, 2024) was used to compute a complete and consistent set of carbonate system variables, as described by Nisumaa et al. (2010). In this dataset the original values were archived in addition with the recalculated parameters (see related PI). The date of carbonate chemistry calculation by seacarb is 2025-08-25.