Obtaining the core temperature of the cable joint is vital to ensure the safe operation of the modern power system with integration. To improve the speed and accuracy of core temperature inversion, this study proposed a non-embedded cable joint temperature inversion method named uniform manifold approximation and projection (UMAP) and the improved sparrow search algorithm (ISSA) optimized the back propagation neural network (BPNN). Firstly, UMAP is used to reduce the feature dimension of sample data input and enhance the data visualization effect. After dimension reduction, the model input features are consistent with the international ampacity calculation standard, and the calculation speed and accuracy of the model are improved. To improve the optimization ability of SSA, the Tent chaotic operator is introduced, and then the ISSA is used to optimize BPNN to address the issue of unstable output and easy falling into a local minimum. At last, the optimization ability and temperature inversion effect of the improved model were compared with other competing algorithms based on the 10 kV cable joint temperature-rise test and CEC2017 benchmark function. The experimental results show that the proposed method shortens the calculation time of the model, and the mean absolute error of temperature inversion is about 0.1°C. The overall performance is the most outstanding, the training data set is unbiased, and the interpretability of the model improves, which can provide a reliable reference for line operation and maintenance personnel.