Rising temperatures and increasing temperature variability are impacting the range and prevalence of mosquito-borne disease. A promising biocontrol technology replaces wild mosquitoes with those carrying the virus-blocking Wolbachia bacterium. Laboratory and field observations show that the most widely used strain, wMel, is adversely affected by heat stress. Here, we examine whether and how climate warming may impact wMel-based replacement. We integrate empirical data on the temperature sensitivity of wMel bacteria into a mechanistic model of population dynamics for the dengue vector Aedes aegypti and use CMIP5 climate projections and historical temperature records from Cairns, Australia to simulate vector control interventions. We show that higher mean temperatures are predicted to lower wMel infection frequency and that extended heatwaves have the potential to reverse the public health benefits of this intervention. Sensitivity analysis probing the thermal limits of wMel replacement reveal that, under existing projections, operational adaptations would be required for heatwaves lasting longer than two weeks. We conclude that this technology is expected to be robust to both the increased mean temperatures and heatwaves associated with near-term climate change in temperate regions. However, more rapid warming or tropical and inland regions that presently feature hotter baselines may challenge these tested limits, requiring further research.