Forecasting the energy demand is essential for network operators to balance the grid, in particular with the increasing share of renewable energy sources. Neural networks, especially deep neural networks, have shown promising results in recent forecasting tasks. However, they often struggle learning periodicities in time series efficiently. In line with the finding that deep learning can be improved with statistical information, we introduce profile neural networks based on the fast and promising convolutional neural networks. The underlying idea of profile neural networks is that decomposing periodic energy time series into a standard load profile, a trend, and a colorful noise module improves the forecasting accuracy. The proposed deep neural network architecture is applied to real-world electricity data from buildings on a university campus, more specifically of one building with strong seasonal variation and one building with weak seasonal variation. The new architecture outperforms current state-of-the-art deep learning benchmark models regarding the forecasting accuracy on forecast horizons of one day and one week-ahead, improving the mean absolute scaled error by up to 25%, as well as regarding the trade-off between training time and accuracy.