Thermal deformation is a major source of positioning error in CNC machines due to nonuniform heat generation and complex temperature variations across different machine components. Accurate prediction of thermal error is challenging because temperature data collected from multiple sensors exhibit nonlinear, noisy, and long-term dependent behavior. In this work, a thermal error prediction framework is proposed using an extended Long Short-Term Memory (xLSTM) network, where critical model hyperparameters are optimized using an Adaptive Grey Wolf Optimizer (AGWO) before model training. The bio-inspired AGWO algorithm adaptively balances exploration and exploitation by dynamically adjusting its control parameters, enabling efficient global search of the hyperparameter space. Temperature data acquired from multiple sensors placed at different locations of the CNC machine are used as input features to capture spatial and temporal thermal effects. The optimized hyperparameters are then employed to train the xLSTM model using gradient-based learning. Experimental results demonstrate that the AGWO-optimized xLSTM model achieves significantly lower thermal prediction error compared to conventional manually tuned and gradient-only approaches. The proposed method improves prediction accuracy, convergence stability, and generalization capability, making it suitable for real-time thermal error compensation in high-precision CNC machining applications. After compensating for the thermal error, the diametral deviation reduces to 95 % and improves the thermal stability of the machine tool. The prediction model capability is proven to be improved using the proposed approach.