The mechanisms that lead to the formation and the disappearance of prominences are poorly understood, at present. An arch-shaped prominence was observed with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on board the Solar and Heliospheric Observatory (SOHO) on 31 March–1 April 1996. The observations were performed at three wave-bands in the Lyman continuum. Ten successive images were obtained at 41-minute time intervals. Based on computed models of Gouttebroze, Heinzel, and Vial (1993), we have determined the temperature distribution of the prominence using the intensity ratio of 876Å and 907Å. The observed time sequence shows that parts of the prominence disappear possibly by heating, while other parts exhibit heating and cooling with apparent outward motion. We model the heat input with the linearized MHD equations using a prescribed initial density and a broad-band spectrum of Alfvén waves. We find a good qualitative agreement with observations. In the model the prominence is heated by the resonant absorption of Alfvén waves with frequencies that match the resonant condition for a particular flux tube structure that is determined by the magnetic field topology and plasma density.