Measurements of the heat load on C (isotropic graphite) and W targets wereperformed in linear steady plasma facility MAP-II (materials and plasma),which produces a low-energy hydrogen plasma 10-20 eV with an electron densityof (1.0-5.0)×1017 m-3. From the measurements of the heatremoved by the target coolant, heat flow to the target and Balmer intensitiesnear the targets we found that the heat load was larger on the C target than Wbecause of higher molecular hydrogen desorption. The population densities ofvibrational levels in the d 3Πu state of molecular hydrogenshifted to higher levels near the C target in the spectroscopy of the Fulcherband. From these results, it was found that molecular hydrogen desorptionplays an important role in the heat load on plasma facing materials and itdepends on the materials, which have different characteristics of hydrogenmolecular desorption and energy states of desorbed hydrogen.