  We adopt Hulth\'en plus Hellmann potential as the quark-antiquark interaction
potential for predicting the mass spectra of heavy mesons. The adopted
potential was made to be temperature-dependent by replacing the screening
parameter with Debye mass.The radial Schr\"odinger equation was analytically
solved using the series expansion method and energy eigenvalues were obtained.
The energy eigenvalues is used to predict the mass spectra of heavy mesons such
as charmonium and bottomonium. Four special cases were considered when some of
the potential parameters were set to zero, resulting in Hellmann potential,
Yukawa potential, Coulomb potential, and Hulth\'en potential, respectively. The
present potential provides satisfying results in comparison with experimental
data and the work of other researchers with a maximum error of 0.034 GeV.
