  We investigate the heating of an erupting prominence and loops associated
with a coronal mass ejection and X-class flare. The prominence is seen in
absorption in EUV at the beginning of its eruption. Later the prominence
changes to emission, which indicates heating of the erupting plasma. We find
the densities of the erupting prominence using the absorption properties of
hydrogen and helium in different passbands. We estimate the temperatures and
densities of the erupting prominence and loops seen as emission features using
the differential emission measure method, which uses both EUV and X-ray
observations from the Atmospheric Imaging Assembly on board Solar Dynamics
Observatory and the X-ray Telescope on board Hinode. We consider synthetic
spectra using both photospheric and coronal abundances in these calculations.
We verify the methods for the estimation of temperatures and densities for the
erupting plasmas. Then we estimate the thermal, kinetic, radiative loss,
thermal conduction, and heating energies of the erupting prominence and loops.
We find that the heating of the erupting prominence and loop occurs strongly at
early times in the eruption. This event shows a writhing motion of the erupting
prominence, which may indicate a hot flux rope heated by thermal energy release
during magnetic reconnection.
