Under global warming, compound drought-heat events (CDHEs) have intensified and pose increasing risks to water resources, ecosystems, and agricultural production, particularly in semi-arid transitional basins. However, the joint-risk characteristics, categorical predictability, and driving mechanisms of CDHEs in the Weihe River Basin remain insufficiently understood. This study develops an integrated analytical framework combining Copula-based risk identification, HydroFusionNet-driven prediction, and potential causal-linkage interpretation to assess CDHEs. First, the Standardized Precipitation Index (SPI) and Standardized Temperature Index (STI) were used to characterize drought and heat anomalies, and multiple Copula functions were applied to quantify the joint occurrence probabilities and return periods of CDHEs under different intensity combinations. Second, HydroFusionNet was developed by integrating temporal embedding, residual convolutional feature extraction, bidirectional recurrent sequence modeling, and Transformer-based global dependency learning to predict CDHE occurrence using meteorological, hydrological, and vegetation-related variables. Finally, Shapley Additive Explanations (SHAP) was combined with convergent cross mapping (CCM) to identify the relative contributions of key drivers and further examine potential causal linkages between major hydrothermal variables and CDHEs. The results show that the frequency of moderate-to-severe heat events in the Weihe River Basin has increased markedly since 2000, and the return period of extreme drought-heat combinations in the North Luohe River subbasin reaches approximately 40-70 years, which is substantially higher than those in other sub-basins. SHAP results indicate that precipitation contributes most to CDHE prediction, accounting for 23.2%-35.8% of the total importance, followed by minimum temperature and mean temperature. CCM analysis further reveals stable hydrothermal coupling among temperature-, moisture-, and vegetation-related variables. Large-scale circulation diagnostics show that CDHE occurrence is significantly and negatively correlated with synchronous AO and with the one-month lagged PNA and PDO; meanwhile, CDHE months are generally associated with lower AO, NAO, and PDO and higher NP and GAT, indicating that regional CDHEs are jointly influenced by local hydrothermal conditions and large-scale background signals.