River water temperature modeling – a time series problem where spatial relations matter – is important to understand our environment. Currently two research directions are present to tackle this problem, viz. Recurrent Neural Networks, namely long short-term memory (LSTM), and Graph-based approaches, which exploit the natural tree structure of rivers. In the present paper, we extend a state-of-the-art LSTM method for water temperature modeling with a Graph Convolutional Network and a Graph Isomorphism Network. This novel combination results in a spatio-temporal neural network which can be applied for node predictions in any graph having nodes with unique identifiers. In the present paper, we apply the novel procedure on the Swiss River Network (a data set with decades of measurements of river temperature and atmospheric variables in Switzerland). In an experimental evaluation we show that the proposed method is robust in convergence and improves the state-of-the-art result by several percentage points in terms of Root Mean Squared Error.