Temperature is a crucial state to guarantee the reliability and safety of a battery during operation. The ability to estimate battery temperature, especially the internal temperature, is of paramount importance to the battery management system for monitoring and thermal control purposes. In this paper, a data-driven approach combining the RBF neural network (NN) and the extended Kalman filter (EKF) is proposed to estimate the internal temperature for lithium-ion battery thermal management. To be specific, the suitable input terms and the number of hidden nodes for the RBF NN are first optimized by a two-stage stepwise identification algorithm (TSIA). Then, the teaching-learning-based optimization (TLBO) algorithm is developed to optimize the centres and widths in every neuron of basis function. After optimizing the RBF NN model, a battery lumped thermal model is adopted as the state function with the EKF to filter out the outliers of the RBF model and reduce the estimation error. This data-driven approach is validated under four different conditions in comparison with the linear NN models. The experimental results demonstrate that the proposed RBF data-driven approach outperforms the other approaches and can be extended to other types of batteries for thermal monitoring and management.