Physics-based ensemble weather prediction models form the backbone of probabilistic operational weather forecasting systems. The ensemble weather forecasts, however, suffer from systematic biases and inappropriate dispersion, which can be corrected by applying statistical postprocessing techniques. In this work, we apply a Transformer based on self-attention to postprocess forecasts of solar radiation from the EUPPBenchmark dataset. Our method results in a \(5.3\%\) improvement in CRPS over the raw forecasts, realizes a significant increase of \(25 \%\) in ensemble spread, and outperforms a classical member-by-member method employed as a competitive baseline. Finally, we convert these postprocessed weather forecasts into solar power predictions, highlighting the potential of the Transformer for practical renewable energy applications.