  We present numerical simulations of the acoustic-phonon-limited mobility,
$\mu_{ac}$, and phonon-drag thermopower, $S^{g}$, in two-dimensional electron
gases confined in MgZnO/ZnO heterostructures. The calculations are based on the
Boltzmann equation and are made for temperatures in the range 0.3-20 K and
sheet densities $0.5$-$30\times 10^{15}$ m$^{-2}$. The theoretical estimations
of $\mu_{ac}$ are in good agreement with the experiment without any adjustable
parameters. We find that the magnitude of $\mu_{ac}$ is dramatically decreased
in relation to GaAs based heterostructures. The phonon-drag thermopower,
$S^{g}$, which according to Herring's expression is inversely proportional to
$\mu_{ac}$ is severely increased exceeding 200 mV/K at $T=5$ K depending on
sheet density. The giant values of $S^{g}$ lead to a strong improvement of the
figure of merit $ZT$ at low temperatures. Our findings suggest that MgZnO/ZnO
heterostructures can be candidates for good thermoelectric materials at
cryogenic temperatures.
