Efficient trajectory prediction through the numerical solution of ordinary differential equations (ODEs) is essential for implementing model predictive control (MPC), especially when dealing with complex dynamic systems. However, the inherent sequential nature of ODE solvers often introduces significant computational bottlenecks, restricting MPC applicability in real-time industrial scenarios. This work proposes an advanced strategy to accelerate trajectory prediction by integrating three synergistic techniques: reusing previous trajectory solutions, parallelizing computations, and applying interpolation. By utilizing the previous trajectory solution as an initial guess (warm-start), the proposed approach substantially reduces computational effort and enhances solver convergence. Parallelization further accelerates prediction by distributing computational tasks across multiple processors, exploiting modern computational architectures. Interpolation refines intermediate solutions between discrete time points, ensuring continuity, accuracy, and smooth transitions. The effectiveness of the combined strategy is demonstrated through a case study involving a detailed continuous steel reheating furnace model characterized by complex thermal dynamics and high-dimensional stiff ODEs. Results show significant computational speed-up while preserving prediction accuracy, highlighting the potential of the approach for real-time MPC deployment. This research contributes to bridging the gap between computationally demanding model-based control strategies and their practical implementation in advanced industrial process control systems.