Traditional fruit tree cultivars are an important source of agricultural biodiversity. These genotypes are well adapted to the regions where they grow, and their fruits offer distinctive features compared to the commercial cultivars that are frequently grown. We analyzed the adaptation prospects of seven sweet cherry cultivars grown in Zaragoza (Spain) to future climate conditions. We first delineated chilling and forcing phases using Partial Least Squares (PLS) regression to correlate phenology records with daily accumulations of chill and heat during the months preceding flowering. We then calculated chill requirements using three chill models (Chilling Hours, Utah and Dynamic) and forcing requirements using one heat model (Growing Degree Hours, GDH). Results indicated that the chilling and forcing requirements ranged between 26.1 and 60.2 CP (chill portions) and from 5473 to 8030 GDH, respectively. We then assessed the cultivars’ potential to adapt to a warmer future using climate projections and comparing the chill requirements with the expected chill accumulation under two global warming scenarios, RCP4.5 (effective reduction of greenhouse gas emissions) and RCP8.5 (very high greenhouse gas emissions), by two time horizons, 2050 and 2085, with temperature projections from fifteen Global Climate Models (GCM). These projections established that chill accumulation has consistently decreased over the last 30 years, but temperate trees have shown regular breaking of dormancy, bud burst and blooming. Future chill levels are expected to continue decreasing given the sustained warming trend, so there is no guarantee that sufficient winter chill will be observed in the medium to long term if the warming trend continues. For three out of the seven cultivars we analyzed, most global climate models predict medium or low risks by 2050 and 2085 under the RCP4.5 scenario. Under the RCP8.5 scenario, particularly by the end of the 21st century (i.e. 2085), four of the cultivars with high chill needs are expected to not to meet their chill requirements very often.