  Prominences are large magnetic structures in the corona filled by cool plasma
with fast evolving fine structure. We aim to better understand the plasma
conditions in the fine structure of a quiescent prominence including two
transient horns observed at the bottom of the cavity using the high-resolution
spectrograph IRIS and the MulTi-Raies (MTR) spectrograph of the THEMIS in the
Canary Islands. We analysed the spectra obtained in H-alpha by THEMIS and MgII
by IRIS and compare them with a grid of 23940 1D radiative transfer models
which include a prominence-to-corona transition region (PCTR). The full
observed profiles of MgII in each pixel are fitted completely by synthesised
profiles with xRMS (Cross RMS; an improved version of the rolling root mean
square (rRMS) method). When the RMS is below a certain threshold value, we
recover the plasma conditions from the parameters of the model best fitting the
observed line profile. This criterion is met in two regions (the horns and edge
of the prominence) where the line profiles can generally be described as single
peaked. The 1D models suggest that two different kinds of model atmospheres
correspond to these two regions. The region at the edge is found to be fitted
mainly with isothermal and isobaric models, while the other area (the horns) is
seen to be fitted with models with a PCTR that have optical thicknesses <5. In
the prominence edge, the theoretical relationship between the integrated
intensities in H-alpha and MgII is verified and corresponds to low emission
measure values. In these regions the electron density is ~10^10 cm^{-3}, while
it is one order of magnitude less in the horn regions. In the horns, we find
some profiles are best fitted with models with high mean temperatures. This
suggests that the hot PCTR found in the horns could be interpreted as
prominence plasma in condensation phase at the bottom of the coronal cavity.
