  We consider the thermoelectric response of chaotic or disordered quantum dots
in the limit of phase-coherent transport, statistically described by random
matrix theory. We calculate the full distribution of the thermoelectric
coefficients (Seebeck $S$ and Peltier $\Pi$), and the thermoelectric figure of
merit $ZT$, for large open dots at arbitrary temperature and external magnetic
field, when the number of modes in the left and right leads ($N_{\rm L}$ and
$N_{\rm R}$) are large. Our results show that the thermoelectric coefficients
and $ZT$ are maximal when the temperature is half the Thouless energy, and the
magnetic field is negligible. They remain small, even at their maximum, but
they exhibit a type of universality at all temperatures, in which they do not
depend on the asymmetry between the left and right leads $(N_{\rm L}-N_{\rm
R})$, even though they depend on $(N_{\rm L}+N_{\rm R})$.

Mesoscale and Nanoscale Physics;Chaotic Dynamics;Quantum Physics