Note the use of the term removed instead of melted—as in, any excess water is moved to where it can't cause trouble, either through the use of advanced technology (space elevators, et cetera) or for the sake of having a simplistic model.
Almost exactly 1 year ago, I asked a very similar question on Quora, to which I got only this answer, which I vigorously disagreed with here. Nevertheless, the use of the term "under present climatic conditions" may have led him to assume the climate is also somehow held constant rather than being influenced by the changes (just not by anthropogenic greenhouse gases), and the massive scope of the question probably discouraged more people from answering. I hope this wording will be more clear.
That answer assumed a rapid and catastrophic re-attainment of the status quo. My disagreement comes from several factors that would act in tandem to warm its climate:
- Lower elevation within the troposphere. The lapse rates described in the paper Altitude dependence on the ice sheet surface climate imply that ignoring other factors, Vostok Station would be 23.6–26.5 °C warmer without the elevation of the ice depending on the season and assumptions made, while the temperature at Amundsen–Scott would increase by 17.7–21.5 °C. This effect would be less the closer the glacial surface is to the subglacial terrain or sea level.
- Greater solar heating. Ice can reflect 90% or more of its incident solar energy, while bare rock typically has a far lower albedo, with around 10–40% of solar energy reflected, with the rest absorbed to heat up itself and the air. Open water has an extremely low albedo, with only ~6% of solar energy reflected. Even at the South Pole, provided skies are clear and atmospheric conditions are ideal, solar heating alone can sustain liquid water for about 84 days†. The actual decrease in (year-round average) albedo wouldn't be as significant due to seasonal snow/ice cover, but as solar energy is massively concentrated in the summer at Antarctic latitudes, the effective albedo would still be much less.
- Topography and other effects allowing warm ocean currents and air masses to move southward. The general warming of the Antarctic would cause the maximum-density Antarctic Circumpolar Current to move southward, with subtropical currents such as the Brazil, Agulhas, and East Australian currents pushing southward and providing a Gulf Steam-like influence. The lower elevation of the interior would also allow (warm) weather fronts from lower latitudes to penetrate deep into the continent.
As implied all throughout this, there would be negative feedbacks causing reglaciation, and said glaciation would stop at some point, but the point of contention is when and where, i.e. how negative the second derivative of glacial area is. So, with all the factors taken into account, what would be the answer? Is Barry Lewis correct or not?
†This was roughly calculated by combining solar angle with the Stefan-Boltzmann law at the albedo of open water, with an estimate of the atmospheric absorption and reflection given absolutely ideal atmospheric conditions adjusted by angle.