Fused deposition modelling (FDM) is increasingly used to produce high-performance polymer components; however, the mechanical performance of printed parts is often limited by weak interlayer adhesion, void formation, and residual thermal stresses. In this study, the effects of nozzle temperature, bed temperature, and post-treatment annealing temperature on the tensile and flexural strength of FDM-printed polyether ether ketone (PEEK) were investigated and optimized using Response Surface Methodology (RSM). A face-centred central composite design was employed to evaluate the individual, quadratic, and interaction effects of the three thermal parameters. The results showed that post-treatment annealing temperature was the most influential factor, contributing 56.48% to tensile strength and 52.73% to flexural strength, followed by nozzle temperature, which contributed 30.56% and 30.15%, respectively. Bed temperature showed a comparatively smaller individual effect; however, its interaction with nozzle temperature significantly influenced both tensile and flexural strength. The confirmation experiment performed at 200 °C post-treatment temperature, 414 °C nozzle temperature, and 142 °C bed temperature produced a tensile strength of 55.65 MPa and a flexural strength of 81.08 MPa, with prediction errors of 5.63% and 4.08%, respectively. SEM fracture analysis provided qualitative evidence that improved thermal processing reduced interlayer separation and visible void-related defects while promoting a more cohesive fracture morphology. These improvements are attributed to enhanced interlayer fusion, possible polymer-chain diffusion across layer boundaries, and thermal-stress relaxation during annealing. The findings demonstrate that thermal-parameter optimization and post-treatment annealing can improve the mechanical performance of FDM-printed PEEK within the investigated processing window.