The thermopower of the molecular state in a double quantum dot is studied u
sing a mixed model, which combines the classical capacitance model and a va
lence-electron approach. Our calculations show that close to the triple poi
nts where the resonances of the two dots intersect, there are additional st
eplike structures in the thermopower that result from coupling of the "topm
ost" electronic states. Far away from the triple points, we find that, with
increasing detuning, the steplike structures shift toward the center of tw
o neighboring Coulomb blockade oscillations, while very far away from the t
riple points, the transport resembles that of a single dot of lower electro
static energy. Our results are in qualitative agreement with experimental f
indings on the conductance of Blick et al.