The optimization of energy consumption during asphalt mixture production and compaction is a challenge in producing durable, sustainable, and environmentally friendly asphalt products. This study investigated the effects of crude palm oil (CPO) and/or tire pyrolysis oil (TPO) on shear viscosity and mixing and compaction temperatures of asphalt. Moreover, the possibility of using response surface methodology (RSM) and machine learning (ML) to develop predictive models for the shear viscosity and mixing and compaction temperatures of CPO- and/or TPO-modified asphalt was studied and compared. The results showed that the mixing and compaction temperatures significantly decreased with increasing CPO and TPO, and the shear viscosity consequently declined because of the light components, resulting in softer binders. However, at 5% of both materials, a balance between the required temperatures and a similar or better viscosity compared to the base asphalt were demonstrated. RSM analysis showed that CPO had a significant effect on the viscosity and production temperatures of the base and modified asphalts compared with TPO, which had no significant effects. The developed predictive models based on RSM exhibited a correlation coefficient (R²) of more than 0.82 for all responses. In addition, it was found that extreme gradient boosting (XGB) regression was the best among all evaluated algorithms for predicting shear viscosity, whereas random forest regression (RFR) was the best for mixing and compaction temperatures, with R² values greater than 0.93. The performance evaluations of XGB and RFR showed extremely small differences between the predicted and experimental data. ML outperformed RSM in terms of prediction accuracy.