Climate change poses a threat to species with temperature-dependent sex determination (TSD). A recent study on green sea turtles (Chelonia mydas) at the northern Great Barrier Reef (GBR) showed a highly female-skewed sex ratio with almost all juvenile turtles being female. This shortage of males might eventually cause population extinction, unless rapid evolutionary rescue, migration, range shifts, or conservation efforts ensure a sufficient number of males. We built a stochastic individual-based model inspired by C. mydas but potentially transferrable to other species with TSD. Pivotal temperature, nest depth, and shading were evolvable traits. Additionally, we considered the effect of crossbreeding between northern and southern GBR, nest site philopatry, and conservation efforts. Among the evolvable traits, nest depth was the most likely to rescue the population, but even here the warmer climate change scenarios led to extinction. We expected turtles to choose colder beaches under rising temperatures, but surprisingly, nest site philopatry did not improve persistence. Conservation efforts promoted population survival and did not preclude trait evolution. Although extra information is needed to make reliable predictions for the fate of green sea turtles, our results illustrate how evolution can shape the fate of long lived, vulnerable species in the face of climate change.