Anthropogenically induced global climate change has important implications for marine ecosystems with unprecedented ecological and economic consequences. Climate change will include the simultaneous increase of temperature and CO₂ concentration in oceans. However, experimental manipulations of these factors at the community scale are rare. In this study, we used an experimental approach in mesocosms to analyse the combined effects of elevated CO₂ and temperature on macroalgal assemblages from intertidal rock pools. Our model systems were synthetic assemblages of varying diversity and understory component and canopy species identity. We used assemblages invaded by the non‐indigenous canopy forming alga Sargassum muticum and assemblages with the native canopy species Cystoseira tamariscifolia. We examined the effects of both climate change factors on several ecosystem functioning variables (i.e. photosynthetic efficiency, productivity, respiration and biomass) and how these effects could be shaped by the diversity and species identity of assemblages. CO₂ alone or in combination with temperature affected the performance of macroalgae at both individual and assemblage level. In particular, high CO₂ and high temperature (20°C) drastically reduced the biomass of macroalgal assemblages and affected their productivity and respiration rates. The identity of canopy species also played an important role in shaping assemblage responses, whereas species richness did not seem to affect such responses. Species belonging to the same functional effect group responded differently to the same environmental conditions. Data suggested that assemblages invaded with S. muticum might be more resistant in a future scenario of climate change. Thus, in a future scenario of increasing temperature and CO₂ concentration, macroalgal assemblages invaded with canopy‐forming species sharing response traits similar to those of S. muticum could be favoured.