## 1 Introduction
[25] leveraged a modified transformer-based model (MT-LSTR) which was trained on simulated data to predict temperature dynamics effectively. Meanwhile, [PERSON] et al. [26; 27] proposed two distinct data-driven strategies: a Gradient Boosting Decision Tree (GBDT) ensemble to model nonlinear relationships between stator and rotor temperatures and a model-free SVR method with a linear kernel. This study reduced reliance on domain expertise while reliably estimating temperatures. XGBoost (eXtreme Gradient Boosting, version 1.7.0) is a powerful machine learning method that has gained attention in engineering applications for optimizing systems and improving predictions [28; 29]. Recent research has further demonstrated its versatility. [PERSON] et al. [30] developed an AI-Enabled Energy-Saving Strategy (AIESS) combining XGBoost and Genetic Algorithms (GAs) to minimize energy consumption in electro-hydraulic systems. Similarly, [PERSON] et al. [31] employed XGBoost to enhance photovoltaic power generation forecasting, leveraging its ability to handle nonlinear relationships between environmental variables and energy generation. [PERSON] and [PERSON] [32] integrated XGBoost with FEA to refine torque characteristics, predict torque ripple, and adjust operational parameters. [PERSON] et al. [33] advanced temperature prediction using XGBoost. Their method integrated data normalization, Bayesian hyperparameter optimization, and model training. [PERSON] et al. [34; 35] further extended XGBoost's utility in sustainable motor design by developing surrogate models to accelerate the optimization of interior PMSMs. Collectively, these studies highlight the potential of machine learning (particularly XGBoost) to enhance precision, reduce computational demands, and adapt to dynamic thermal conditions in PMSMs. While existing methods address specific operational scenarios, three critical limitations persist under complex driving conditions: (1) insufficient generalization, (2) accuracy-computation efficiency tradeoffs, and (3) limited real-time adaptability. This study proposes a novel hybrid method combining machine learning and meta-heuristic algorithms to establish a prediction model for the rotor temperature of PMSMs. The model is based on XGBoost and optimizes three hyperparameters (number of trees, tree depth, and learning rate) using the RIME (Rime optimization algorithm). By adaptively enhancing XGBoost according to the data scale and input samples, a hybrid model with high learning ability and generalization capability is established, named RIME-XGBoost. The input features for modeling include easily monitored variables of the PMSM, such as motor speed, torque, currents, and voltages in the d/q coordinate system, with rotor temperature as the target variable. Prediction experiments are conducted using these features. To test the characteristics and applicability of the developed model, experiments are carried out using medium-scale data with large temperature fluctuations and small-sample data collected in high-temperature ranges. For comparison, three recently published hybrid models are selected, i.e., Random Forest (RF) optimized by the Slime Mould Algorithm (SMA), BiGRU optimized by the Snake Optimizer (SO), and Support Vector Regression (SVR) optimized by the Equilibrium Optimizer (EO). The prediction accuracy, stability, and computational efficiency of each model are evaluated using metrics such as Root Mean Square Error (RMSE), Mean Bias Error (MBE), R-squared, and Runtime. This article is organized as follows. Section 2 describes the source, composition, and processing of the experimental data. Section 3 introduces the basic theories of XGBoost and RIME. Section 4 presents the various hybrid models used for comparison and describes the metrics for quantifying the test results. Section 5 investigates the effectiveness and characteristics of RIME-XGBoost using medium-scale and small-scale samples and provides a detailed discussion with the comparison models.