Does Earth risk losing its oceans to space due to global warming?
We know that terrestrial hydrogen reaches space because ultraviolet images reveal
  a halo of hydrogen atoms surrounding the Earth (Fig. 2). Some of these atoms are
  escaping while the rest are trapped. The temperature at Earth’s exobase is typically around
  1000 K, although it varies as the Sun’s ultraviolet output cycles up and down every 11
  years or so. At 1000 K, hydrogen atoms have an average speed of 5 km/sec, which is
  below Earth’s escape velocity of 10.8 km/sec at the exobase. Yet hydrogen atoms still
  manage to escape because many move faster than average. This loss of particles from the
  energetic tail of the speed distribution is called “Jeans’ escape” after James Jeans (from the
  University of Cambridge), who described it mathematically in the early twentieth century.


The escape of planetary atmospheres Catling &amp; Zahnle, Scientific American,2009 1

The exobase is the lower boundary of the exosphere.



I guess that two degrees increase in surface temperature would not make much difference to the $~1000K$ at the exobase.