There are multiple approaches to modeling spot temperatures and spot prices of natural gas in the literature, as well as extensive models for commodity forward curves. However, there is a gap concerning temperature forecasts; these are closely watched by natural gas traders, as they contain vital information to anticipate changes in the natural gas term structure. This paper introduces a three-factor model that jointly describes both natural gas forward prices and temperature forecast dynamics. The model is established based on the Heath–Jarrow–Morton approach acting jointly on the log returns of the gas term structure and forecast differences. The factors are determined by principal component analysis (PCA) on the forward curve of the Dutch natural gas trading hub Title Transfer Facility and Amsterdam temperature forecasts. The PCA results reveal a clear dependency of the gas forward curve on the temperature predictions, which is mainly reflected in the third principal component and factor.