Machine learning (ML)-based predictive techniques are used in conjunction with a game-theoretic approach to predict the thermal behavior of a power electronics package and study the relative influence of encapsulation material properties and thermal management in influencing hotspot temperatures. Parametric steady-state and transient thermal simulations are conducted for a commercially available 1.2 kV/444 A SiC half-bridge module. An extensive databank of 2592 (steady-state) and 1200 (transient) data points generated via numerical simulations is used to train and evaluate the performance of three ML algorithms (random forest, support vector machine and neural network) in modeling the thermal behavior. The parameter space includes the thermal conductivities of the encapsulant, baseplate, heat sink and cooling conditions deployed at the sink; the parametric space covers a variety of materials and cooling scenarios. Excellent prediction accuracies with R2 values > 99.5% are obtained for the algorithms. SHAP (Shapley Additive exPlanations) dependence plots are used to quantify the relative impact of device and heat sink parameters on junction temperatures. We observe that while heatsink cooling conditions significantly influence the steady-state junction temperature, their contribution in determining the junction temperature in dynamic mode is diminished. Using ML-SHAP models, we quantify the impact of emerging polymeric nanocomposites (with high conductivities and diffusivities) on hotspot temperature reduction, with the device operating in static and dynamic modes. Overall, this study highlights the attractiveness of ML-based approaches for thermal design, and provides a framework for setting targets for future encapsulation materials.