The persistence of tropical coral reefs is threatened by rapidly increasing climate warming, causing a functional breakdown of the obligate symbiosis between corals and their algal photosymbionts (Symbiodinium) through a process known as coral bleaching. Yet the potential of the coral-algal symbiosis to genetically adapt in an evolutionary sense to warming oceans is unknown. Using a quantitative genetics approach, we estimated the proportion of the variance in thermal tolerance traits that has a genetic basis (i.e. heritability) as a proxy for their adaptive potential in the widespread Indo-Pacific reef-building coral Acropora millepora. We chose two physiologically different populations that associate respectively with one thermotolerant (Symbiodinium clade D) and one less tolerant symbiont type (Symbiodinium C2). In both symbiont types, pulse amplitude modulated (PAM) fluorometry and high performance liquid chromatography (HPLC) analysis revealed significant heritabilities for traits related to both photosynthesis and photoprotective pigment profile. However, quantitative real-time polymerase chain reaction (qRT-PCR) assays showed a lack of heritability in both coral host populations for their own expression of fundamental stress genes. Coral colony growth, contributed to by both symbiotic partners, displayed heritability. High heritabilities for functional key traits of algal symbionts, along with their short clonal generation time and high population sizes allow for their rapid thermal adaptation. However, the low overall heritability of coral host traits, along with the corals' long generation time, raise concern about the timely adaptation of the coral-algal symbiosis in the face of continued rapid climate warming.