In order to monitor climate change in Switzerland, the Federal Office for the Environment has been measuring river water temperature at 81 water stations for over 40 years. Based on these measurements and the underlying river network, we create a novel graph regression problem with a total of 3,480 graphs. The task is to predict the water temperature of output nodes by using a subset of input nodes. Depending on the subset, this creates challenging information bottlenecks and long-range dependencies. In a first contribution, we set RMSE baselines for four standard Graph Neural Networks (GNNs). Namely, we employ and compare GCN, GIN, GAT, and GraphSAGE architectures with up to 7 layers. In a second contribution, we analyze how noise propagates through such networks. In our evaluation, we observe that the GNN models degenerate more severely than alternative architectures. This empirical result shows that the message passing framework can harm models in presence of noise, a rarely mentioned limitation we would like to address in future research.