We tackle the challenge of spatial prediction for Hilbert data embedded within river networks, where the network’s reticular layout mandates geostatistical approaches employing Stream Distance to capture spatial connectivity stemming from branching. Embedded within Object Oriented Spatial Statistics (O2S2), we present the innovative methodology introduced in [1]; here, the authors conceptualize data as points within a functional embedding space, and devise functional moving average models grounded in the Stream Distance. This methodology allows one to take into account both data and spatial domain geometry, enabling the establishment of a coherent covariance structure and the definition of associated estimators. By analysing summer water temperature profiles along Idaho’s Middle Fork River, our approach showcases its effectiveness in modelling the covariance structure and enhancing forecasting capabilities within the O2S2 paradigm. This investigation offers valuable insights into tailored modeling techniques adept at navigating the complexities of spatially structured data in natural landscapes.