Two-dimensional polarized atomic hydrogen(H down arrow) was adsorbed o
nto a liquid helium surface which was locally cooled much below the te
mperature of the rest of a large sample cell. The steady state conditi
on was obtained by introducing a constant H down arrow flux into the s
ample cell. We measured a bulk density of H down arrow and the change
of heat input due to the introduction of H down arrow flux into the sa
mple cell as a function of the cold spot temperature for various sampl
e cell temperatures and input flux. The cooling mechanism of two-dimen
sional hydrogen was studied and the optimization condition to obtain K
osterlitz-Thouless transition was investigated in this system.