As anthropogenic climate change is an ongoing concern, scientific investigations on its impacts on coral reefs are increasing. Although impacts of combined ocean acidification (OA) and temperature stress (T) on reef-building scleractinian corals have been studied at the genus, species and population levels, there are little data available on how individual corals respond to combined OA and anomalous temperatures. In this study, we exposed individual colonies of Acropora digitifera, Montipora digitata and Porites cylindrica to four pCO2-temperature treatments including 400 μatm-28 °C, 400 μatm-31 °C, 1000 μatm-28 °C and 1000 μatm-31 °C for 26 days. Physiological parameters including calcification, protein content, maximum photosynthetic efficiency, Symbiodinium density, and chlorophyll content along with Symbiodinium type of each colony were examined. Along with intercolonial responses, responses of individual colonies versus pooled data to the treatments were investigated. The main results were: 1) responses to either OA or T or their combination were different between individual colonies when considering physiological functions; 2) tolerance to either OA or T was not synonymous with tolerance to the other parameter; 3) tolerance to both OA and T did not necessarily lead to tolerance of OA and T combined (OAT) at the same time; 4) OAT had negative, positive or no impacts on physiological functions of coral colonies; and 5) pooled data were not representative of responses of all individual colonies. Indeed, the pooled data obscured actual responses of individual colonies or presented a response that was not observed in any individual. From the results of this study we recommend improving experimental designs of studies investigating physiological responses of corals to climate change by complementing them with colony-specific examinations.