The very high temperature contrast between magma/lava and water ice commonly leads to the assumption that significant melting will take place immediately upon magma/lava ice contact, yet observations of active flows show little evidence of voluminous melting upon contact. We use analytical thermal models to reassess the efficiency with which heat can be transferred from magma to ice in three situations: lava flows erupted on top of glacial ice, sill intrusions beneath glacial ice evolving into subglacial lava flows and dyke intrusions into the interiors of glaciers. We find that the maximum ratios of thickness of ice that can be melted to the thickness of magmatic heat source are likely to be ∼2-5 for subaerial lava flows encroaching onto glaciers, ∼6-7 for subglacial lava flows and ∼10 for dykes intruded into glacial ice. Rates of ice melt production are not linear functions of time and flow thickness, however, and this may account for the observations of minimal immediate water release from beneath advancing lava flows. Field observations during future eruptions should be directed at measuring the temperature of released water.