Asymptotic AdS Riemann space-times in five dimensions with a black brane (horizon) sourced by a fully back-reacted scalar field (dilaton) offer—via the holographic dictionary—various options for the thermodynamics of the flat four-dimensional boundary theory, uncovering Hawking–Page, first-order, and second-order phase transitions up to a cross-over or featureless behavior. The relation of these phase structures to the dilaton potential is clarified and illustrating examples are presented. Having in mind applications to QCD, we study probe vector mesons with the goal to figure out conditions for forming Regge-type series of radial excitations and address the issue of meson melting.