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This study investigates the prediction of fine-grained electricity peak demand using coarser-resolution data. Specifically, it addresses whether sparse high-resolution monitoring can inform forecasts of future high-resolution peaks when detailed measurements are unavailable, a question of particular importance for network operators evaluating the replacement of costly monitoring systems with predictive models. We develop models capable of estimating half-hourly maxima and minima from one-minute interval electricity load data using inputs aggregated to 30-minute intervals. Our methodology combines generalized additive models (GAMs) and deep neural networks (DNNs), both widely applied in load forecasting. The analysis includes an in-depth assessment of input feature importance, focusing on load patterns, meteorological variables, and seasonal trends. The proposed approach achieved first place in a data competition organized by Western Power Distribution (WPD), a UK electricity distribution operator. Beyond the competition, we conduct an extended evaluation over an additional 11 months, confirming that our combined model significantly outperforms the benchmark in out-of-sample root mean squared error (RMSE), achieving a 57.4% reduction compared to the competition reference.