The aim of our research was to adapt Chuine’s unified model to estimate the beginning of blooming of three apricot cultivars (‘Ceglédi bíborkajszi’, ‘Gönci magyar kajszi’, and ‘Rózsakajszi C.1406’) in Hungary in the time period 1994–2020. The unified model is based on the collection of chilling and forcing units. The complexity of the model lies in the high number of parameters necessary to run it. Following the work of other researchers, we reduced the number of relevant model parameters (MP) to six. In order to estimate the six MPs, we used a simulated annealing optimization method (known for being effective in avoiding getting stuck in local minima). From the results, we determined the local optimum of six MPs, and the global optimum parameter vector for three apricot cultivars. With these global optimum parameter vectors, the beginning of blooming could be estimated with a root-mean-square error (RMSE) of less than 2.5 days, using the knowledge of the daily mean temperature in the time period 1994–2020.