Hyperbolic heat conduction presents a complex phenomenon that challenges traditional problem-solving approaches. In this study, we propose a methodological problem-solving framework tailored specifically for addressing hyperbolic heat conduction problems. By integrating mathematical modeling, numerical methods, and experimental validation, this framework offers a comprehensive approach to understanding and analyzing heat transfer processes governed by hyperbolic equations. Through a systematic application of the proposed methodology, researchers and engineers can gain valuable insights into the transient behavior of heat conduction in materials exhibiting hyperbolic characteristics, leading to enhanced predictive capabilities and informed decision-making in various engineering applications.