  Using the explicit rational conformal field theory partition functions for
the ${\mathbb Z}_k$ parafermion quantum Hall states on a disk we compute
numerically the thermoelectric power factor for Coulomb-blockaded islands at
finite temperature. We demonstrate that the power factor is rather sensitive to
the neutral degrees of freedom and could eventually be used to distinguish
experimentally between different quantum Hall states having identical electric
properties. This might help us to confirm whether non-Abelian quasiparticles,
such as the Fibonacci anyons, are indeed present in the experimentally observed
quantum Hall states.
