Computer-aided modeling and optimization of thermal energy systems are essential for improving energy efficiency and reducing emissions in industrial processes. The utilization of industrial waste heat offers significant potential but requires accurate modeling of heat transfer processes. Model accuracy and computational performance depend on the selected modeling and optimization approach. Mixed integer nonlinear programming can represent heat transfer with high physical fidelity, including nonlinear relations such as the logarithmic mean temperature difference and temperature-dependent properties, but is associated with high computational effort and convergence challenges. Mixed integer linear programming is widely used in energy system analysis due to its robustness and short solution times, although it requires simplifications of temperature-dependent relationships. Recent developments in mixed integer quadratically constrained programming (MIQCP) provide a promising approach, enabling a more accurate representation through bilinear heat transfer relations while maintaining reasonable solution times. The objective of this work is a systematic comparison of linear, quadratic and nonlinear optimization approaches for the operational optimization of an industrial waste heat recovery system to assess the potential of MIQCP. The models are based on hourly resolved measurement data for two representative one-month periods, one in summer and one in winter. Heat transfer is described using coupled mass and energy balances as well as different levels of approximation of temperature-dependent relationships. Literature-based modeling approaches are implemented for the investigated energy system and comparatively evaluated with respect to accuracy, computational time, implementation complexity and deviation in the calculated optimum. Accuracy is assessed using the root mean square error between model predictions and measured heat transfer, while the deviation in the calculated optimum is determined by transferring the optimization results of each approach to a common reference model for comparative analysis. The preliminary results indicate that MIQCP approaches can achieve higher accuracy than linear models while requiring lower computational effort than fully nonlinear formulations. The findings highlight the potential of MIQCP for the optimization of industrial waste heat recovery systems.