Accurate performance prediction and preventive maintenance of heavy-duty gas turbines are critical for enhancing operational efficiency and reducing downtime. This study proposes an enhanced Deep Operator Network (DeepONet) framework for predicting key performance indicators of gas turbines, including efficiency, heat rate, and power output, to enable condition-based maintenance. The method replaces the conventional trunk network of DeepONet with Transformer, which architecture is capable of dynamically capturing complex temporal dependencies and long-range dependencies in historical data relevant to the prediction target through its self-attention mechanism. Additionally, causal convolutional units are embedded into the branch network to ensure temporal causality. The proposed framework is validated using real-world gas turbine operational data, demonstrating superior prediction accuracy compared to traditional DeepONet models, with the reduction of mean square error and mean absolute error values. The integration of multi-scale temporal modeling and causal constraints effectively addresses challenges posed by nonlinear dynamics, variable coupling in gas turbines. Predictive results are further utilized to quantify performance degradation trends, enabling early fault detection and optimized maintenance scheduling.