If you need to warm it up depends on the depth - at the bottom the ice is not much colder than 0°C due to geothermal flux. So if, say, you only used the hot wat

If you need to warm it up depends on the depth - at the bottom the ice is not much colder than 0°C due to geothermal flux. So if, say, you only used the hot water method for the lowest part, the amount of heat for warming can easily be neglected.