In the subglacial eruption at Gjálp in October 1996 a 6 km long and 500 m high subglacial hyaloclastite ridge was formed while large volumes of ice were melted by extremely fast heat transfer from magma to ice. Repeated surveying of ice surface geometry, measurement of inflow of ice, and a full Stokes 2-D ice flow model have been combined to estimate the heat output from Gjálp for the period 1996–2005. The very high heat output of order 10 6 MW during the eruption was followed by rapid decline, dropping to ∼ 2500 MW by mid 1997. It remained similar until mid 1999 but declined to 700 MW in 1999–2001. Since 2001 heat output has been insignificant, probably of order 10 MW. The total heat carried with the 1.2 × 10 12 kg of basaltic andesite erupted (0.45 km 3 DRE) is estimated to have been 1.5 × 10 18 J. About two thirds of the thermal energy released from the 0.7 km 3 edifice in Gjálp occurred during the 13-day long eruption, 20% was released from end of eruption until mid 1997, a further 10% in 1997–2001, and from mid 2001 to present, only a small fraction remained. The post-eruption heat output history can be reconciled with the gradual release of 5 × 10 17 J thermal energy remaining in the Gjálp ridge after the eruption, assuming single phase liquid convection in the cooling edifice. The average temperature of the edifice is found to have been approximately 240 °C at the end of the eruption, dropping to ∼ 110 °C after 9 months and reaching ∼ 40 °C in 2001. Although an initial period of several months of very high permeability is possible, the most probable value of the permeability from 1997 onwards is of order 10 − 12 m 2. This is consistent with consolidated/palagonitized hyaloclastite but incompatible with unconsolidated tephra. This may indicate that palagonitization had advanced sufficiently in the first 1–2 years to form a consolidated hyaloclastite ridge, resistant to erosion. No ice flow traversing the Gjálp ridge has been observed, suggesting that it has effectively been shielded from glacial erosion in its first 10 years of existence.