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Fruit and nut trees production is an important activity across the southwest United States and this production is greatly impacted by the local climate. Temperature is the main environmental factor influencing the growth and the productivity of the fruit and nut trees as it affects the trees’ physiology and the vulnerability of flower bud, flowers, and young fruit and nut to the low temperatures or spring frost. The objective of the present study is to estimate the chilling and heat accumulation of fruit and nut trees across New Mexico. Three study sites as Fabian Garcia, Los Lunas, and Farmington were considered and climate variables were collected at hourly time step. The Utah model and the Dynamic model were used to estimate the accumulated chilling while the Forcing model was used for the heat accumulation. The possible fruit and nut trees endodormancy and ecodormancy periods were also determined at the study sites. The results obtained chilling hours of 715 ± 86.60 h at Fabian Garcia, 729.53 ± 41.71 h at Los Lunas, and 828.95 ± 83.73 h at Farmington using the Utah model. The accumulated chill portions during trees’ endodormancy was 3.12 ± 3.05 CP at Fabian Garcia, 42.23 ± 5.08 CP at Los Lunas, and 56.14 ± 1.84 CP at Farmington. The accumulated heat was 8735.52 ± 1650.91 GDH at Fabian Garcia, 7695.43 ± 212.90 GDH at Los Lunas, and 5984.69 ± 2353.20 GDH at Farmington. The fruit and nut trees are at no risk of bud flowers vulnerability at Fabian Garcia while they are under high risk of bud flowers and or young fruit and nut vulnerability to low temperatures early spring as hourly temperature can still drop below 0 °C in April at the end of ecodormancy and flower blooming and young fruits and nuts development stage at Los Lunas and Farmington. Severe weather, especially frost conditions during winter and early spring, can be a significant threat to sustainable nut and fruit production in the northern New Mexico while high chilling requirement fruit and nut trees might not meet chill requirements in the southern New Mexico.