We show theoretically that the Coulomb drag rate between two parallel quasi-two-dimensional electron gases with equal Fermi velocities is substantially enhanced by the coupled acoustic and optic plasmon modes at temperatures $T\ensuremath{\gtrsim}0.2{T}_{F}$ (where ${T}_{F}$ is the Fermi temperature) for experimentally relevant parameters. The acoustic mode causes a sharp upturn in the scaled drag rate with increasing temperature at $T\ensuremath{\approx}0.2{T}_{F}$. Other experimental signatures of the plasmon-dominated drag rate are a ${d}^{\ensuremath{-}3}$ dependence on the well separation $d$ and a peak as a function of relative densities at matched Fermi velocities.