  We report on simulations of the formation of the first stars in the Universe,
where we identify regions of hot atomic gas (fH2 < 10-6) at densities above
10-14 g/cc, heated to temperatures ranging between 3000 and 8000 K. Within this
temperature range atomic hydrogen is unable to cool effectively. We describe
the kinetic and thermal characteristics of these regions and investigate their
origin. We find that these regions, while small in total mass fraction of the
cloud, may be dynamically important over the accretion timescale for the
central clump in the cloud, particularly as a chemical, rather than radiative,
mechanism for clearing the polar regions of the accretion disk of material and
terminating accretion along these directions. These inherently
three-dimensional effects stress the need for multi-dimensional calculations of
protostellar accretion for reliable predictions of the masses of the very first
stars.
