The energy consumption of buildings’ Heating, Ventilation, and Air Conditioning (HVAC) systems accounts for approximately 15%-20% of the total societal energy consumption, indicating significant potential for energy-saving design. Accurate indoor temperature prediction in buildings is crucial for the pre-planning, coordinated control, and energy management of HVAC systems. However, building indoor temperature is influenced by spatial variability due to weather conditions and building structure, as well as by seasonal changes, occupant activities, and equipment usage patterns, which exhibit both long and short cycles, making long-term precise prediction challenging. This paper proposes a multi-step indoor temperature prediction model based on Gated Recurrent Unit (GRU) neural networks, leveraging correlation analysis of relative parameters and temporal feature construction. By employing data resampling and moving window averaging methods, historical cycle features of related variables and indoor temperature sequences are constructed. Additionally, a multi-step synchronous prediction neural network output structure is established, effectively enhancing the model's robustness. The performance of the optimized model is validated on the smart building open-source dataset PLEIAData. Multi-model comparative experiments and ablation experiments demonstrate that the proposed GRU-F1-F2-M model improves MAE by 16.15% and 38.03% and RMSE by 15.36% and 57.89% compared to the optimized single-step GRU model and commonly used statistical model SARIMA, respectively.