The microwave (MW) resonance absorption and decay heating of surface electrons (SEs) on liquid <$E ~sup 4 roman He> are theoretically studied for the vapor atom scattering regime. The decay heating is shown to be an essential occurrence of a MW resonance experiment appearing even at low excitation rates. It strongly affects the occupancies of surface levels and the broadening of resonance lines long before the absorption suturation condition is reached. Contrary to the model of cold SEs usually used for description of the MW resonance, the new theory leads to MW absorption saturation when only a very small fraction of electrons (less than 10 %) is left on the ground and the first excited levels.

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