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The recovery of bioactive compounds from medicinal plants depends on complex interactions among process variables. This study investigated heat-assisted extraction (HAE) of Catharanthus roseus leaves and developed predictive models describing the effects of extraction temperature (OT), solid-to-liquid ratio (S/L), and extraction time (ET) on total phenolic content (TPC), antioxidant activity (AA), and extraction yield (EY). After preliminary one-factor-at-a-time (OFAT) screening, a three-factor, three-level Box–Behnken design (BBD) under response surface methodology (RSM) was applied. Quadratic models were developed and validated using analysis of variance (ANOVA), coefficients of determination, and diagnostic plots. All models were highly significant (p < 0.0001) with strong predictive power (R² > 0.99). Temperature was the dominant factor affecting TPC and AA, while ET strongly influenced EY. Bootstrap resampling confirmed model robustness and parameter stability. Monte Carlo simulations provided probabilistic insights, showing greater uncertainty in TPC predictions than in EY. Sensitivity analysis revealed that phenolic recovery was most responsive to temperature, whereas EY depended on solvent availability and contact time. Overall, RSM modeling with reliability and uncertainty analyses offers a robust framework for understanding extraction dynamics and serves as a predictive tool for process optimization and industrial scale-up.