Understanding the behavior of large outlet glaciers draining the Greenland Ice Sheet is critical for assessing the impact of climate change on sea level rise. The flow of marine‐terminating outlet glaciers is partly governed by calving‐related processes taking place at the terminus but is also influenced by the drainage of surface runoff to the bed through moulins, cracks, and other pathways. To investigate the extent of the latter effect, we develop a distributed surface‐energy‐balance model for Helheim Glacier, East Greenland, to calculate surface melt and thereby estimate runoff. The model is driven by data from an automatic weather station operated on the glacier during the summers of 2007 and 2008, and calibrated with independent measurements of ablation. Modeled melt varies over the deployment period by as much as 68% relative to the mean, with melt rates approximately 77% higher on the lower reaches of the glacier trunk than on the upper glacier. We compare melt variations during the summer season to estimates of surface velocity derived from global positioning system surveys. Near the front of the glacier, there is a significant correlation (on >95% levels) between variations in runoff (estimated from surface melt) and variations in velocity, with a 1 day delay in velocity relative to melt. Although the velocity changes are small compared to accelerations previously observed following some calving events, our findings suggest that the flow speed of Helheim Glacier is sensitive to changes in runoff. The response is most significant in the heavily crevassed, fast‐moving region near the calving front. The delay in the peak of the cross‐correlation function implies a transit time of 12–36 h for surface runoff to reach the bed.