We study the thermoelectric transport properties through a quantum wire, modeled on a tight-binding linear chain, with an embedded gate-defined quantum dot. We obtain the thermopower, thermal conductance and electrical conductance with a lateral Fano resonance, linked to a many-body renormalized quantum dot resonant level at the edge of the conduction band strongly hybridized with the van Hove singularity of the one-dimensional density of states of the lead; this resonance appears above the Kondo temperature and is due to a quantum interference thermally activated. We discuss the possibility of practical application of the system to a mesoscopic cooling process and thermopower generators, based on the thermoelectric figure of merit and thermal conductance values. Our results for the thermal transport properties are consistent with those obtained previously for electronic transport.