Marine heatwaves are becoming more frequent, widespread and severe, causing mass coral bleaching and mortality. Natural adaptation may be insufficient to keep pace with climate warming, leading to calls for selective breeding interventions to enhance the ability of corals to survive such heatwaves, i.e., their heat tolerance. However, the heritability of this trait–a prerequisite for such approaches–remains unknown. We show that selecting parent colonies for high rather than low heat tolerance increased the tolerance of adult offspring (3–4-year-olds). This result held for the response to both 1-week +3.5 °C and 1-month +2.5 °C simulated marine heatwaves. In each case, narrow-sense heritability (h2) estimates are between 0.2 and 0.3, demonstrating a substantial genetic basis of heat tolerance. The phenotypic variability identified in this population could theoretically be leveraged to enhance heat tolerance by up to 1 °C-week within one generation. Concerningly, selective breeding for short-stress tolerance did not improve the ability of offspring to survive the long heat stress exposure. With no genetic correlation detected, these traits may be subject to independent genetic controls. Our finding on the heritability of coral heat tolerance indicates that selective breeding could be a viable tool to improve population resilience. Yet, the moderate levels of enhancement we found suggest that the effectiveness of such interventions also demands urgent climate action. Marine heatwaves can have severe impact on corals populations. This study demonstrates that selective breeding could quickly enhance coral tolerance to short-term heat stress by up to 1 °C. This has potential to mitigate some impacts of climate change, however urgent climate action is still needed.