The governing hydrological processes are expected to shift under climate change in the alpine regions of Switzerland. This raises the need for more adaptive and accurate methods to estimate river flow. In high-altitude catchments influenced by snow and glaciers, short-term flow forecasting is challenging, as the exact mechanisms of transient melting processes are difficult to model mathematically and are poorly understood to this date. Machine learning methods, particularly temporally aware neural networks, have been shown to compare well and often outperform process-based hydrological models on medium and long-range forecasting. In this work, we evaluate a Long Short-Term Memory neural network (LSTM) for short-term prediction (up to three days) of hourly river flow in an alpine headwater catchment (Goms Valley, Switzerland). We compare the model with the regional standard, an existing process-based model (named MINERVE) that is used by local authorities and is calibrated on the study area. We found that the LSTM was more accurate than the process-based model on high flows and better represented the diurnal melting cycles of snow and glacier in the area of interest. It was on par with MINERVE in estimating two flood events: the LSTM captures the dynamics of a precipitation-driven flood well, while underestimating the peak discharge during an event with varying conditions between rain and snow. Finally, we analyzed feature importances and tested the transferability of the trained LSTM on a neighboring catchment showing comparable topographic and hydrological features. The accurate results obtained highlight the applicability and competitiveness of data-driven temporal machine learning models with the existing process-based model in the study area.