  We investigate the time dependent thermal relaxation of a two-dimensional
electron system in the fractional quantum Hall regime where ballistic phonons
are used to heat up the system to a non-equilibrium temperature. The thermal
relaxation of a 2DES at $\nu=1/2$ can be described in terms of a broad band
emission of phonons, with a temperature dependence proportional to $T^4$. In
contrast, the relaxation at fractional filling $\nu=2/3$ is characterized by
phonon emission around a single energy, the magneto-roton gap. This leads to a
strongly reduced energy relaxation rate compared to $\nu=1/2$ with only a weak
temperature dependence for temperatures 150 mK $< T <$ 400 mK.
