Increasing sea‐surface temperatures and ocean acidification (OA) are impacting physiologic processes in a variety of marine organisms. Many sea anemones, corals and jellies in the phylum Cnidaria form endosymbiotic relationships with Symbiodinium spp. (phylum Dinoflagellata) supply the hosts with fixed carbon from photosynthesis. Much work has focused on the generally negative effects of rising temperature and OA on calcification in Symbiodinium‐coral symbioses, but has not directly measured symbiont photosynthesis in hospite or fixed carbon translocation from symbiont to host. Symbiodinium species or types vary in their environmental tolerance and photosynthetic capacity; therefore, primary production in symbiotic associations can vary with symbiont type. However, symbiont type has not been identified in a large portion of Symbiodinium−cnidarian studies. Future climate conditions and OA may favor non‐calcifying, soft‐bodied cnidarians, including zoanthids. Here we show that two zoanthid species, Palythoa sp. and Zoanthus sp., harboring different symbiont types (C1 and A4), had very different responses to increased temperature and increased partial pressure of CO2 (pCO2), or dissolved CO2, and low pH. Thermal stress did not affect carbon fixation or fixed carbon translocation in the Zoanthus sp./A4 association, and high pCO2/low pH increased carbon fixation. In contrast, both thermal stress and high pCO2/low pH greatly inhibited carbon fixation in the Palythoa sp./C1 association. However, the combined treatment of high temperature and high pCO2 increased carbon fixation relative to the treatment of high temperature alone. Our observations support the growing body of evidence that demonstrates that the response of symbiotic cnidarians to thermal stress and OA must be considered on a host‐specific and symbiont‐specific basis. In addition, we show that the effects of increased temperature and pCO2 on photosynthesis may change when these two stressors are combined. Understanding how carbon fixation and translocation varies among different host−symbiont combinations is critical to predicting which Symbiodinium associations may persist in warm, acidified oceans.