Here we report on measurements of the spin-Seebeck effect of GaMnAs over an extended temperature range alongside the thermal conductivity, specific heat, magnetization, and thermoelectric power. The amplitude of the spin-Seebeck effect in GaMnAs scales with the thermal conductivity of the GaAs substrate and the phonon-drag contribution to the thermoelectric power of the GaMnAs, demonstrating that phonons drive the spin redistribution. A phenomenological model involving phonon-magnon drag explains the spatial and temperature dependence of the measured spin distribution.