This paper presents a novel forecasting methodology based on neural networks and second-generation wavelets, and an example of application of such methodology for forecasting the oil temperature of an actual power transformer. The proposed method consists on selecting the variables with the highest correlation concerning the magnitude to be predicted (in situations featuring multiple variables), selecting the most appropriate second-generation wavelet from a set of candidate lifting wavelet transforms to smooth each variable's data and using the values smoothed by the selected second-generation wavelet to train the considered neural network. The authors applied the proposed methodology to predict the oil temperature of an existing transformer for four days and for one month using field data collected during four years of equipment operation. The obtained results indicate that selecting the most appropriate second-generation wavelet considering different selection techniques and using them to smooth the input variables significantly reduce the forecasting errors. The application of the proposed approach to forecast the oil temperature from the field-collected data using a long short-term memory neural network considering different batch sizes, neuron numbers and second-generation wavelet selection techniques decreased the average forecasting errors presented by using just the considered long short-term memory network by up to eleven times. The innovations of this proposal about literature are the use of correlation-based variable selection techniques given improving neural network forecasting accuracy, which is unprecedented in transformer insulating oil temperature forecasting applications, and the employment of SGWs to smooth the network's inputs to increase the accuracy of the model significantly. For the application case study presented in this research, the minor average forecasting errors in percentage to predict the four-day and one-month future temperature were, respectively, 0.012 and 0.326%. Also, for one month of forecasting, the average error in degrees Celsius was less than 0.2.