Woody perennial species from temperate regions fall dormant during the cold winter season to avoid unfavourable conditions. To break out of dormancy and eventually flower, they must fulfil cultivar-specific chilling and heat requirements. Phenology analysis can clarify the climatic requirements of tree cultivars and thus provide critical information to ensure the future viability of orchards in warm growing regions, where warmer winters are expected as a result of climate change. We used Partial Least Squares (PLS) regression to correlate first bloom dates of 4 local and 3 foreign pistachio (Pistacia vera L.) cultivars with daily chill and heat accumulation (quantified with the Dynamic Model and Growing Degree Hours Model, respectively) for 18-year records (1997–2016) from Sfax, Tunisia. PLS outputs allowed delineation of the chilling phase, during which high chill accumulation was correlated to early bloom, and the forcing phase, when this was true for high heat accumulation. Both phases showed discontinuities. During September and October, high heat accumulation appeared to first have a bloom-delaying effect, followed by a bloom-advancing effect, indicating that temperature during dormancy induction may affect bloom dates. Chilling requirements were estimated between 32.1 ± 2.3 and 33.3 ± 2.2 Chill Portions and heat requirements between 9974 ± 198 and 12,738 ± 235 Growing Degree Hours. This study revealed limitations of the Dynamic Model, which is often considered the most accurate among commonly used models, in the warm Tunisian climate. High temperatures during the chilling phase had a significant bloom-delaying effect on all pistachio cultivars. Low chill accumulation was related to very low yields and associated with zero production in 1995, 2001 and 2007. Low flowering percentage, high bud fall percentage, long and inhomogeneous bloom, and co-occurrence of several phenological stages on the same branch were symptoms of lack of chill in 2016.