We present a study of the thermopower S and the dimensionless figure of merit ZT in molecules sandwiched between gold electrodes. We show that for molecules with side groups, the shape of the transmission coefficient can be dramatically modified by Fano resonances near the Fermi energy, which can be tuned to produce huge increases in S and ZT. This shows that molecules exhibiting Fano resonances have a high efficiency of thermoelectric cooling which is not present for conventional ungated molecules with only delocalized states along their backbone.