  We study the thermoelectric transport of a small metallic island weakly
coupled to two electrodes by tunnel junctions. In the Coulomb blockade regime,
in the case when the ground state of the system corresponds to an even number
of electrons on the island, the main mechanism of electron transport at lowest
temperatures is elastic cotunneling. In this regime, the transport coefficients
strongly depend on the realization of the random impurity potential or the
shape of the island. Using the random-matrix theory, we calculate the
thermopower and the thermoelectric kinetic coefficient and study the statistics
of their mesoscopic fluctuations in the elastic cotunneling regime. The
fluctuations of the thermopower turn out to be much larger than the average
value.
