The present work explores the feasibility of single-phase friction riveting on unreinforced thermoplastics. In single phase, the load is kept constant throughout the process, avoiding the forging phase with higher axial force, used in the conventional process. This process variant can constitute an answer when payload restrictions exist. The results demonstrate the feasibility of single-phase friction riveting on unreinforced polyetherimide plates joined by AA2024 rivets with 5 mm of diameter. A Box-Behnken design of experiments and analysis of variance were used to set parameter matrix and understand the correlations between parameters and joint properties. A large variation of the mechanical energy input was observed (151–529 J). Over-deformation and material rupture were observed in higher energy conditions. Lower energy input yielded a bell-shaped rivet plastic deformation, corresponding to the best performance. The maximum process temperatures varied between 461 and 509 °C. This friction riveting process variant allowed a considerable high mechanical strength to be achieved, with ultimate tensile force of 7486 N, comparable with the two-phase friction riveting process, albeit applying lower axial forces, such as 2400 N. Within the investigated conditions, this study proves the feasibility of the single-phase process, achieving good global mechanical performance and energetically efficient conditions, without forging phase.