The technology of filling drinks without preservatives (such as fresh juices, iced tea drinks, and vitaminized drinks) is carried out using hot filling. Mainly due to the production costs and lower carbon footprint, polyethylene terephthalate (PET) bottles are increasingly used in this technology. In this paper, the main aim is to describe and interpret the results of statistical analysis of the influence of the temperature of the blow mold in the SBM (stretch blow molding) process and the method of hot filling on the macroscopic and microscopic bottle properties. The macroscopic bottle properties were defined by the thickness profile, pressure resistance, thermal stability, and the coefficients of blowing kinetics. In addition, the influence of the SBM process on the microscopic PET material properties (in the bottle) relative to the microscopic preform properties was analyzed. The microscopic properties were defined by the degree of crystallite, density, and relaxation of the amorphous phase of the PET material. For this purpose, response surface experiments were performed for the two analyzed factors, i.e., the temperature of the blow mold and the method of hot filling. The sample size was investigated to determine the minimum number of repetitions (number of bottles in the measurement series) required to achieve acceptable measurement uncertainty. The research conducted shows that, despite fulfilling the postulate of acceptable measurement uncertainty, in terms of the power of ANOVA (analysis of variance) in DOE (design of experiment), the accepted number of bottles in the measurement series is too small. The tests of the bottle material density, material crystallite, and relaxation of amorphous phase relative to the preform material density, material crystallite, and relaxation of amorphous phase show that microcavity effects occur during the deformation of the PET material, and that these are associated with the orientation of the microstructure. The blow kinetics study shows that there is a gradient of flow of the bottle material over the thickness of the bottle wall during blowing, and it has been deduced that the air temperature between the blow mold and the wall of the blown bottle has an impact on the kinetics of blowing the bottle.