Quasi-two-dimensional (Q2D) Coulomb interactions between plasmons and phonons in a GaAs quantum well are studied numerically. Based on the dielectric continuum model, the plasmon-confined phonon coupling and plasmon-symmetric () interface phonon coupling are considered. By using renormalized phonon propagators, six branches involving plasmon-like and phonon-like modes are obtained and used to study the effect on the hot-carrier average energy-loss rate (AELR). Plasmon-like modes are demonstrated to enhance the AELR around the sheet carrier density of 1011 cm-2 due to a significant contribution of the plasmon-symmetric (+) interface phonon coupled mode. The importance of interface phonon modes on the plasmon-phonon coupling (PPC) is also indicated. If the interface phonon is not considered, the AELR enhancement due to the PPC will not appear. In addition, the carrier temperature is found to be important for the AELR enhancement. As the carrier temperature is as low as possible, the AELR enhances more remarkably because the effect of reabsorption of plasmon-like modes for hot carriers (hot-plasmon effect) can be greatly suppressed.