Transient heat transfer topology optimization is critical for enhancing thermal management in applications like energy systems and aerospace, but it faces prohibitive computational costs due to time-domain simulations. This paper proposes a novel hybrid reduced-order framework that integrates modal acceleration method (MAM) and K-Means++ clustering correction to overcome these limitations. The approach eliminates steady-state errors via pseudo-static vector compensation and repairs transient oscillations by selecting key temperature patterns as supplementary bases, avoiding reliance on full-model snapshots. Leveraging CPU parallel computing, the framework accelerates large-scale sparse matrix operations and sensitivity analysis. Numerical examples, including 2D thermal control and 3D metal hydride reactor fin design, demonstrate efficiency gains of up to 465 times for problems with over 100,000 degrees of freedom, while maintaining accuracy in convergence and topology results. The method enables practical, high-fidelity optimization of transient thermal structures.