Context. We study the physics of erupting prominences in the core of coronal mass ejections (CMEs) and present a continuation of a previous analysis.Aims. We determine the kinetic temperature and microturbulent velocity of an erupting prominence embedded in the core of a CME that occurred on August 2, 2000 using the Ultraviolet Coronagraph and Spectrometer observations (UVCS) on board the Solar and Heliospheric Observatory (SOHO) simultaneously in the hydrogen Lα and C iii lines. We develop the non-LTE (departures from the local thermodynamic equilibrium – LTE) spectral diagnostics based on Lα and Lβ measured integrated intensities to derive other physical quantities of the hot erupting prominence. Based on this, we synthesize the C iii line intensity to compare it with observations.Methods. Our method is based on non-LTE modeling of eruptive prominences. We used a general non-LTE radiative-transfer code only for optically thin prominence points because optically thick points do not allow the direct determination of the kinetic temperature and microturbulence from the line profiles. The input parameters of the code were the kinetic temperature and microturbulent velocity derived from the Lα and C iii line widths, as well as the integrated intensity of the Lα and Lβ lines. The code runs in three loops to compute the radial flow velocity, electron density, and effective thickness as the best fit to the Lα and Lβ integrated intensities within the accuracy defined by the absolute radiometric calibration of UVCS data.Results. We analyzed 39 observational points along the whole erupting prominence because for these points we found a solution for the kinetic temperature and microturbulent velocity. For these points we ran the non-LTE code to determine best-fit models. All models with τ 0 (Lα ) ≤ 0.3 and τ 0 (C iii) ≤ 0.3 were analyzed further, for which we computed the integrated intensity of the C iii line using a two-level atom. The best agreement between computed and observed integrated intensity led to 30 optically thin points along the prominence. The results are presented as histograms of the kinetic temperature, microturbulent velocity, effective thickness, radial flow velocity, electron density, and gas pressure. We also show the relation between the microturbulence and kinetic temperature together with a scatter plot of computed versus observed C iii integrated intensities and the ratio of the computed to observed C iii integrated intensities versus kinetic temperature. Conclusions. The erupting prominence embedded in the CME is relatively hot with a low electron density, a wide range of effective thicknesses, a rather narrow range of radial flow velocities, and a microturbulence of about 25 km s-1 . This analysis shows a disagreement between observed and synthetic intensities of the C iii line, the reason for which most probably is that photoionization is neglected in calculations of the ionization equilibrium. Alternatively, the disagreement might be due to non-equilibrium processes.