Here, we report the optimization of scrap tire rubber (STR) pyrolysis in a fixed-bed reactor for the production of pyrolytic oil (py-oil). Special attention was focused on determining the effects of the temperature and gas residence time on the py-oil and aromatic yields, as well as the optimal range of operating conditions for their maximization. For that purpose, an experimental 4 × 3 factorial design was applied. The maximum py-oil yield obtained was 42.6 mass% at high temperatures and short gas residence times (560–600 °C and 10–18 s, respectively). In contrast, the maximum aromatic concentration (25.6 mass%) was obtained at moderate operating conditions (450–500 °C and 18–20 s). The analysis of variance revealed that the temperature is the most statistically significant variable in py-oil production while, for the nitrogen volumetric flow, only a combined effect with the temperature was observed. In contrast, in terms of the aromatic yield, both the temperature and gas volumetric flow were found to be statistically significant variables. The models provided determination coefficients (R2) close to 0.90, indicating good precision in the predictions.