This study presents the development and optimization of a deep learning model based on Long Short-Term Memory (LSTM) networks to predict short-term hourly electricity demand in Córdoba, Argentina. Integrating historical consumption data with exogenous variables (climatic factors, temporal cycles, and demographic statistics), the model achieved high predictive precision, with a mean absolute percentage error of 3.20\% and a determination coefficient of 0.95. The inclusion of periodic temporal encodings and weather variables proved crucial to capture seasonal patterns and extreme consumption events, enhancing the robustness and generalizability of the model. In addition to the design and hyperparameter optimization of the LSTM architecture, two complementary analyses were carried out: (i) an interpretability study using Random Forest regression to quantify the relative importance of exogenous drivers, and (ii) an evaluation of model performance in predicting the timing of daily demand maxima and minima, achieving exact-hour accuracy in more than two-thirds of the test days and within abs(1) hour in over 90\% of cases. Together, these results highlight both the predictive accuracy and operational relevance of the proposed framework, providing valuable insights for grid operators seeking optimized planning and control strategies under diverse demand scenarios.