Polymer nanocomposites (PNCs), particularly those enhanced with graphene fillers, show significant promise for improving thermal conductivity in applications such as electronics, energy storage, and aerospace. However, accurately predicting their thermal behavior remains challenging due to the complex multiscale interactions between fillers, polymer matrices, and interfacial regions. This study proposes a novel data-driven framework that integrates Gaussian Process Regression (GPR), sensitivity analysis, correlation analysis, and quantitative causal inference to model and interpret the thermal conductivity of polymer graphene-enhanced composites (PGECs). The GPR model demonstrates strong predictive performance (R2 = 0.8931) while also providing calibrated uncertainty estimates. Sensitivity and correlation analyses identify matrix conductivity and filler volume fraction as dominant factors influencing thermal transport. To move beyond associative insights, causal inference is applied, revealing that thermal matrix, volume fraction, and aspect ratio have direct causal impacts on conductivity, whereas other variables such as Kapitza resistance and graphene conductivity do not. By combining stochastic multiscale modeling with causal reasoning, this approach enhances both predictive accuracy and interpretability, offering a robust framework for material design and performance optimization.