We investigate spectral behavior of phonon spectral functions in an interacting multi-component hot carrier plasma. Spectral analysis of various phonon spectral functions is performed considering carrier-phonon channels of polar and nonpolar optical phonons, acoustic deformation-potential, and piezoelectric Coulomb couplings. Effects of phonon self-energy corrections are examined at finite temperature within a random phase approximation extended to include the effects of dynamic screening, plasmon-phonon coupling, and local-field corrections of the plasma species. We provide numerical data for the case of a photo-generated electron-hole plasma formed in a wurtzite GaN. Our result shows the clear significance of the multiplicity of the plasma species in the phonon spectral functions of a multi-component plasma giving rise to a variety of spectral behaviors of carrier-phonon coupled collective modes. A useful sum rule on the plasma-species-resolved dielectric functions is also found.