With the transition of energy systems toward multi-energy complementarity and intelligent operation, efficient modeling and multi-energy flow (MEF) analysis in electricity–heat integrated energy systems (IES) have become a critical research focus. To address the high complexity and limited dynamic adaptability of traditional physics-based approaches, this study proposes a data-driven MEF modeling method based on long short-term memory (LSTM) networks, aiming to improve modeling efficiency and engineering applicability. The model is trained and evaluated using a simulation dataset generated from real historical climate data of Jinan City, covering an entire local heating season with hourly resolution. Furthermore, its robustness is tested under temperature-deviation scenarios to assess resilience to data noise, reflecting practical conditions such as regional temperature variations. The proposed approach offers a promising tool for real-time optimal dispatch of IES under complex climatic conditions, enhancing both the practicality and robustness of MEF analysis.