  We explore the thermodynamics of AdS$_5$ black holes in two models: i) an
improved holographic QCD model with a simple dilaton potential, and ii) the
St\"uckelberg model in 5D. In the former case, by applying techniques of
singular perturbation theory, we obtain a resummation of the naive expansion at
high temperatures, providing a good fit to the lattice data for the trace
anomaly. In the latter, we find a solution of the equations of motion by
considering an expansion in the conformal dimension of the current associated
to the gauge field.
