Accurate Short-term forecasting of gusts at 10 m above ground level is challenging because gridded meteorological variables exhibit persistence, nonstationarity, and abrupt transitions. This study proposes a Temporal Adaptive Difference Polynomial Network (TADPN) using 8760 hourly records from a representative Nanjing grid point in 2025. Surface and pressure-level predictors are temporally aligned ECMWF IFS HRES 9 km fields retrieved through the default Best Match option of the Open-Meteo Historical Weather API, with a 12 h input window. TADPN uses the current gust as a persistence anchor and decomposes the forecast increment into a basic-trend component and a difference polynomial perturbation component. The basic branch uses all 60 variables, whereas the perturbation branch constructs current states, first- and second-order differences, signed-square terms, and within-variable interactions from 18 wind-related variables, with variable- and term-level soft gates. Strictly chronological three-fold rolling validation yields mean MAE, RMSE, and $R^2$ values of 0.4197 m s⁻¹, 0.6079 m s⁻¹, and 0.9373. TADPN reduces MAE by 11.88–29.88% relative to nine baselines. Ablation and significance analyses support the perturbation branch and difference-based features, demonstrating a lightweight and interpretable framework for hourly single-grid gust forecasting.