Accurate prediction of heat transfer in composite materials with complex microstructures is essential for the design and optimization of advanced aerospace, energy, and multifunctional engineering systems. Recent advances in physics-informed machine learning offer new pathways for modeling such systems without relying on extensive labeled datasets or traditional mesh-based numerical schemes. This work presents two complementary physics-informed frameworks— a multi-subnet Physics-Informed Neural Network (Ms-PINN) for transient conduction and a physics-informed finite-difference U-Net (FD-U-Net) for steady-state conduction—both designed to handle heterogeneous, multi-phase composite microstructures. For transient heat transfer, the proposed Ms-PINN[1] employs a modular architecture with domain-specific subnets, each governing the temperature within a distinct material phase. Temperature continuity and heat-flux continuity conditions are imposed at all material interfaces, enabling the model to accurately capture interactions between matrix and inclusions of varying shapes, quantities, and thermophysical properties. The influence of collocation-point sampling strategies on predictive accuracy is systematically examined. The resulting Ms-PINN demonstrates excellent agreement with finite-difference solutions for transient heat-transfer problems in composites with complex inclusions. For steady-state problems, the proposed FD-U-Net[2] directly maps microstructure images to temperature fields by embedding finite-difference formulations into the loss function of an convolutional architecture. This design enforces physical consistency while eliminating the need for temperature labels. Model performance is evaluated with respect to finite-difference kernel iterations, batch size, and loss-function. Compared with both conventional finite-difference and data-driven U-Nets, the FD-U-Net achieves superior accuracy and computational efficiency. The approach naturally generalizes to multiphase composites and those containing internal heat sources. By integrating a post-processing module, homogenized thermal properties can also be extracted directly from microstructure images. Together, these physics-informed machine-learning frameworks demonstrate powerful and complementary capabilities for computing and interpreting heat-transfer behavior in composites, providing scalable tools for microstructure-level thermal analysis and property prediction.