The continuous increase in industrialized sustainable development and energy demand, particularly in the use of steam, highlights the critical importance of efficient energy forecasting for sustainability. While current deep learning models have proven effective, they often involve numerous hyperparameters that are challenging to control and optimize. To address these issues, this research presents an innovative deep learning model, automatically fine-tuned using an improved RIME optimization algorithm (IRIME), with the aim of enhancing accuracy in energy forecasting. Initially, the bidirectional gated recurrent unit (BiGRU) exhibited promising results in prediction tasks but encountered difficulties in handling the complexity of high-dimensional time-series data related to industrial steam. To overcome this limitation, a bidirectional temporal convolutional network (BiTCN) was introduced to more effectively capture long-term dependencies. Additionally, the integration of a multi-head self-attention (MSA) mechanism enabled the model to more accurately identify and predict key features within the data. The IRIME-BiTCN-BiGRU-MSA model achieved outstanding predictive performance, with an R2 of 0.87966, MAE of 0.25114, RMSE of 0.34127, and MAPE of 1.2178, outperforming several advanced forecasting methods. Although the model is computationally complex, its high precision and potential for automation offer a promising tool for high-precision forecasting of industrial steam emissions. This development supports broader objectives of enhancing energy efficiency and sustainability in industrial processes.