Two-dimensional polarized atomic hydrogen(H down arrow) was adsorbed onto a liquid helium surface which was locally cooled much below the temperature of the rest of a large sample cell. The steady state condition was obtained by introducing a constant H down arrow flux into the sample 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 sample cell as a function of the cold spot temperature for various sample cell temperatures and input flux. The cooling mechanism of two-dimensional hydrogen was studied and the optimization condition to obtain Kosterlitz-Thouless transition was investigated in this system.