Naturally heat-resistant coral populations hold significant potential for facilitating coral reef survival under rapid climate change. However, it remains poorly understood whether they can acclimatize to ocean warming when superimposed on their already thermally-extreme habitats. Furthermore, it is unknown whether they can maintain their heat tolerance upon larval dispersal or translocation to cooler reefs. We test this in a long-term mesocosm experiment using stress-resistant corals from thermally-extreme reefs in NW Australia. We show that these corals have a remarkable ability to maintain their heat tolerance and health despite acclimation to 3-6°C cooler, more stable temperatures over 9 months. However, they are unable to increase their bleaching thresholds after 6-months acclimation to +1°C warming. This apparent rigidity in the thermal thresholds of even stress-resistant corals highlights the increasing vulnerability of corals to ocean warming, but provides a rationale for human-assisted migration to restore cooler, degraded reefs with corals from thermally-extreme reefs.