We have optically detected hydrogen atoms adsorbed on the surface of liquid helium, a system relevant for the study of Base degeneracy in two dimensions. The atoms are excited by 121.6 nm light and detected both in fluorescence and in absorption. The optical spectrum of the adsorbed hydrogen atoms was not known a priori. It shows a resonance that is much broader than that of a hydrogen atom in vacuo, and it is shifted to lower frequencies. From the fluorescence intensity we determine that we have reached a surface density corresponding to one atom per square De Broglie wavelength. This means that our experiments take place at the edge of quantum degeneracy. In the regime where the adsorption isotherm is known we can use the measured hydrogen densities to infer the temperature of the helium surface. We use this information to determine the thermal conductance between the surface and the bulk of liquid helium. We find quantitative agreement between the measured temperature drops and the prediction of ripplon-phonon coupling theory.