  We show that it is possible and rather efficient to compute at non-zero
temperature the thermoelectric characteristics of Coulomb blockaded fractional
quantum Hall islands, formed by two quantum point contacts inside of a
Fabry-Perot interferometer, using the conformal field theory partition
functions for the chiral edge excitations. The oscillations of the thermopower
with the variation of the gate voltage as well as the corresponding
figure-of-merit and power factors, provide finer spectroscopic tools which are
sensitive to the neutral multiplicities in the partition functions and could be
used to distinguish experimentally between different universality classes. We
also propose a procedure for measuring the ratio r=v_n/v_c of the Fermi
velocities of the neutral and charged edge modes for filling factor \nu=5/2
from the power-factor data in the low-temperature limit.
