The aim of this study was to investigate the mechanical and thermal properties of composite pipes based on epoxy resin and glass fibers produced by filament winding (FW) technology. Epoxy resins are widely used polymers in FW composite structures. The thermal characterization of the neat epoxy resin, curing, and post-curing characteristics for the determination of polymerization and glass transition temperature was performed, which is important for the mechanical properties of polymer composite pipes. In the present work, the applicability of the full factorial experimental design in predicting the hoop tensile and compressive strengths of glass fiber/epoxy resin composite pipes was investigated. The composite pipes in accordance with the 23 full factorial experimental design by using of three parameters and two levels of variation were prepared. The winding speed of the composites was taken to be the first factor, the second was the fiber tension, and the third was winding angle. To approximate the response, i.e., the mechanical properties of the composite pipes within the study domain, the first-order linear model with the interaction was used. The influence of each individual factor to the response function was established, as well as the influence of the interaction of the two and three factors. Additionally, those results were completed with the thermal characterization of the polymer composite pipes. From received results from mechanical and thermal characterization, it was concluded that the properties of composite specimens were highly affected by the analyzed parameters in filament winding technology. It was found that the estimated first-degree regression equation with the interaction gave a very good approximation of the experimental results of the hoop tensile and the compressive strengths of composite pipes within the study domain.