In polar environments, the thermoviscous behavior and heat dissipation characteristics of deck hydraulic systems are severely affected, resulting in response delays and increased failure risk during high-load operations such as anchor retrieval. To address the limited availability of polar field test samples and the multi-scale nature of oil-temperature responses—featuring short-term abrupt variations and slow-varying hysteresis—this study proposes a Multi-Scale Attention Transformer (MSA-Transformer). Through parallel multi-scale attention branches, the model collaboratively captures both transient and gradual dynamics, thereby improving prediction robustness under polar extreme cold conditions. Based on anchor-retrieval test data collected in Genhe, China’s Cold Pole, at −30 °C, −35 °C, and −40 °C, a dataset containing 18 load cycles was constructed. Experimental results based on 5-fold stratified cross-validation results show that the MSA-Transformer achieves the best performance across evaluation metrics, attaining an average coefficient of determination (R²) of 0.9119 along with the lowest error rates (MAE, RMSE, MSE) on the test set, thereby outperforming LSTM, CNN-LSTM, and the standard Transformer. This work provides an effective tool for state prediction, maintenance optimization, and anomaly early warning in polar deck hydraulic systems, supporting the intelligent health management of hydraulic equipment.