Abnormal current conditions such as overload, harmonics, non-periodic disturbances, and direct current (DC) components frequently occur in low-voltage electrical lines. These anomalies are the primary causes of temperature rise in conductors, significantly increasing the risk of electrical fires. To achieve accurate identification of overheating causes in low-voltage lines, a method integrating parameter-optimized variational mode decomposition (VMD) with a bidirectional long short-term memory (BiLSTM) enhanced by the convolutional block attention module (CBAM) was proposed. The golden jackal optimization (GJO) algorithm was employed to jointly optimize the key parameters of VMD for multi-modal decomposition of current signals. Multi-dimensional entropy features were subsequently extracted from the most relevant intrinsic mode functions (IMFs) to construct a time-series feature dataset. The CBAM module was incorporated to enhance the model’s sensitivity to relevant abnormal features, improving the BiLSTM’s capability to model time-series patterns under complex disturbances. Experimental results demonstrate that the proposed method achieves an identification accuracy of 95.87%, significantly outperforming four mainstream models: LSTM, BiLSTM, CNN-LSTM, and extreme gradient boosting (XGBoost). This confirms the superior classification performance and robustness of the method. It is concluded that the study provides an effective technical path for early warning of electrical fire hazards and shows promising potential for practical applications.