Holographic models that consider classical vector fields in a 5-d background provide effective descriptions for heavy vector meson spectra. This is true both in vacuum and a thermal medium, such as quark gluon plasma. However, the manner in which these phenomenological models work is unclear. In particular, what is the role of the fifth dimension, and what is the relation between the holographic 5-d background and physical (4-d) heavy mesons? Hadrons, in contrast to leptons, are composite particles with some internal structure that depends on the energy at which they are observed. In this study, a static meson is represented by a heavy quark-antiquark pair with an interaction described by a Nambu Goto string existing in the same 5-d background that provides field solutions leading to masses and decay constants of charmonium states. The resulting interaction potential is linear for large distances, with a string tension consistent with the effective Cornell potential. Introducing temperature $\textit{T}$ in the background, it is found for the $J/\psi$ case that there is a deconfining transition at some critical value of $\textit{T}$. The obtained results indicate that the 5-d background effectively represents the internal structure of the (static) charmonium (quasi) states.