Anthropogenic greenhouse gas emissions are triggering changes in global climate and warming the ocean. This will affect many marine organisms, particularly those with high site fidelity and habitat temperature preferences, such as humpback whales on their breeding grounds. To study the impacts of a warming ocean on marine organisms, large-scale projections of climatic variables are crucial. Global models are of 0.25 - 1° (~25-100 km) resolution, and not ideal to predict localized changes. Here, we provide 0.05° resolution (~5 km) sea surface temperature (SST) projections, statistically downscaled using the delta method. We illustrate the shifting isotherms of the critical 21 and 28°C boundaries, which border the climatic envelope that humpback whales prefer for their breeding grounds, over the course of the 21st century on a decadal temporal resolution. Results show by the end of the 21st century, 35% of humpback whale breeding areas will experience SSTs above or within 1°C of current thresholds if present-day social, economic, and technological trends continue (‘middle of the road’ CMIP6 greenhouse gas trajectory SSP2-RCP4.5). This number rises to 67% under the scenario describing rapid economic growth in carbon-intensive industries (‘fossil-fueled development’ CMIP6 greenhouse gas trajectory SSP5-RCP8.5). These projections highlight the importance of reducing global greenhouse gas emissions and minimizing further SST increases to preserve ecological integrity of humpback whale breeding areas. In this context, our results emphasize the need to focus on protection of critical ocean habitat and to provide high-resolution climate data for this purpose.