S-wave states of charmonium and bottomonium are described using bottom-up AdS/QCD. We propose a holographic model that unifies the description of masses and decay constants, leading to a precise match with experimental data on heavy quarkonia. Finite temperature effects are considered by calculating the current-current spectral functions of heavy vector mesons. The identification of quasiparticle states as Breit-Wigner resonances in the holographic spectral function was made. We develop a prescription to subtract background contributions from the spectral function to isolate the Breit-Wigner peak. The quasiparticle holographic thermal evolution is described, allowing us to estimate the melting temperature for vector charmonia and bottomonia. Our holographic model predicts that J/Psi melts at 415 MeV (similar to 2.92T(c)) and Upsilon melts at 465 MeV (similar to 3.27T(c)).