  We study thermoelectric transport properties of fractional quantum Hall
systems based on exact diagonalization calculation. Based on the relation
between thermoelectric response and thermal entropy, we demonstrate that
thermoelectric Hall conductivity $\alpha_{xy}$ has powerlaw scaling
$\alpha_{xy} \propto T^{\eta}$ for gapless composite Fermi-liquid states at
filling number $\nu=1/2$ and $1/4$ at low temperature ($T$), with exponent
$\eta \sim 0.5$ distinctly different from Fermi liquids. The powerlaw scaling
remains unchanged for different forms of interaction including Coulomb and
short-range ones, demonstrating the robustness of non-Fermi-liquid behavior at
low $T$. In contrast, for $1/3$ fractional quantum Hall state, $\alpha_{xy}$
vanishes at low $T$ with an activation gap associated with neutral collective
modes rather than charged quasiparticles. Our results establish a new
manifestation of the non-Fermi-liquid nature of quantum Hall fluids at finite
temperature.
