This research develops a unified framework for simulating conjugate heat transfer (CHT) problems involving fluid-solid interfaces in a high-performance computing (HPC) environment. Traditional methods face two significant challenges: computational load imbalances when solving the Navier-Stokes equations for fluids and heat conduction equations for solids, and the complexity of resolving the interface at fluid-solid interfaces. To address these, we propose an innovative approach that builds upon our previous work on the immersed boundary method (IBM) [1,2]. The framework unifies the governing equations for conduction and convection by setting zero velocity and uniform pressure inside the solid, allowing direct application of the compressible Navier-Stokes solver for CHT problems. At the fluid-solid interface, the Locally One-Dimensional CHT model is developed to calculate the interface temperature as a weighted average of fluid and solid temperatures using thermal conductivities and the distance. This approach ensures energy conservation, simplifies implementation, and maintains numerical stability, making it both robust and user-friendly for practical engineering applications, particularly in cases with significant thermal conductivity differences. To handle large-scale simulations efficiently, a hierarchical data structure is utilized to represent complex geometries, enabling seamless computation on massively parallel systems. Validation against benchmark problems, such as natural convection and heat conduction around cylinders, demonstrates the accuracy of the method in predicting temperature and velocity fields. Additionally, the framework is applied to a real-world engineering problem: simulating CHT in a system with a rotating fan and a complex heat sink design. The results showcase the capability of the framework to handle intricate geometries and dynamic conditions, providing valuable insights for thermal engineering optimization.