In this study, a computational framework is developed to determine the optimal operating parameters for a condenser heat exchanger featuring a helically coiled tube, integrated into a pyrolysis-based bioenergy unit. A physics-based mathematical model of counter-current heat transfer is constructed, incorporating an energy balance for the cold-side coolant, the logarithmic mean temperature difference, and an overall heat-transfer coefficient that explicitly accounts for cumulative thermal resistances, as well as the thermodynamic conditions of phase transition formalized via the Clausius–Clapeyron equation. The problem of selecting the operating point is formulated as a constrained physics-based optimization, aimed at maximizing the heat-transfer rate while minimizing the mass flow rate of the cooling water, and satisfying thermo-hydraulic constraints (prevention of boiling in the coil, adherence to admissible temperature limits, a prescribed pressure-drop bound, and attainment of condensation). To reduce computational cost, physics-based Bayesian optimization is employed using a surrogate model based on a Gaussian process and the expected-improvement acquisition function, implemented in Python with the scikit-optimize library. Within the cooling-water mass-flow range of 0.01–0.05 kg/s, a pronounced optimum is identified at approximately 0.03 kg/s, corresponding to a maximum heat duty of about 4389 W. The results confirm the applicability of the proposed methodology for engineering regime tuning, constructing Pareto trade-offs, and subsequent integration into a digital twin of the condensation subsystem.