Subglacial eruptions are often associated with rapid penetration of overlying ice and release of large flow rates of water as jökulhlaups. Observations of recent subglacial eruptions indicate rapid syn-eruptive ice melting within liquid-filled subglacial cavities, but quantitative descriptions of possible heat transfer processes need to be developed. Calculations of heat flux from the ice cavity fluid to the melting ice surface indicate that up to 0.6 MW m⁻² may be obtained for fluids undergoing single-phase free convection, similar to minimum estimates of heat flux inferred from observations of recent eruptions. Our model of boiling two-phase free convection in subglacial cavities indicates that much greater heat fluxes, in the range 3–5 MW m⁻², can be obtained in the vent region of the cavity and may be increased further by momentum transfer from the eruption jet. Rapid magma-water heat transfer from fragmented magma is needed to sustain these heat fluxes. Similar heat fluxes are anticipated for forced convection of subcooled cavity water induced by momentum transfer from an eruption jet. These heat fluxes approach those required to explain jökulhlaup flow rates and rapid ice penetration rates by melting in some, but not all recent eruptions.