To meet the growing demand of electrical dispatch, accurate prediction of a dynamic thermal rating (DTR) for transmission lines is crucial. However, the uncertainty of DTR caused by weather data imbalance constraints poses a risk to secure grid operation. To this end, a secure probabilistic interval prediction model is developed to tap potential DTR using bootstrap plus-guided time-series generative adversarial networks (TimeGAN) and spatiotemporal graph network (STGN), called BP-G²NN. The TimeGAN is used to augment the data to solve the weather data imbalance problem. And the STGN model is developed to dynamically strengthen the weight of the model to the key potential feature. In addition, the designed BP strategy restricts the frequency of maximum DTR exceeding the upper bound of prediction intervals and solves the inherent problem of quantile crossings. The simulation experiments using real data verify the validity of the model for DTR decisions.