  We scrutinize various holographic estimations of the deconfinement
temperature within the bottom-up AdS/QCD models. A special emphasis is put on
the recent idea of isospectral potentials in the holographic approach. It is
demonstrated that different models from an isospectral family (i.e., the models
leading to identical predictions for the spectrum of hadrons with fixed quantum
numbers) result in different predictions for the deconfinement temperature.
This difference is found to be quite small in the scalar glueball channel but
very large in the vector meson channel which is often used for fixing
parameters of holographic models. The observed stability in the former case
clearly favors the choice of the glueball channel for thermodynamic predictions
in AdS/QCD models, with the scalar glueball trajectory being taken from lattice
simulations and used as a basic input in improved versions of the Soft Wall
holographic model.
