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This paper develops a trustworthy deep learning model that considers electricity demand (G) and local climate conditions. The model utilises Multi-Head Self-Attention Transformer (TNET) to capture critical information from G, to attain reliable predictions with local climate (rainfall, radiation, humidity, evaporation, and maximum and minimum temperatures) data from Energex substations in Queensland, Australia. The TNET model is then evaluated with deep learning models (Long-Short Term Memory LSTM, Bidirectional LSTM BILSTM, Gated Recurrent Unit GRU, Convolutional Neural Networks CNN, and Deep Neural Network DNN) based on robust model assessment metrics. The Kernel Density Estimation method is used to generate the prediction interval (PI) of electricity demand forecasts and derive probability metrics and results to show the developed TNET model is accurate for all the substations. The study concludes that the proposed TNET model is a reliable electricity demand predictive tool that has high accuracy and low predictive errors and could be employed as a stratagem by demand modellers and energy policy-makers who wish to incorporate climatic factors into electricity demand patterns and develop national energy market insights and analysis systems.