  Metal-string complexes in the quasi-1D framework may play an important role
in molecular electronics by serving not only as nanoscale interconnects but
also as active functional elements for nanoelectronic devices. However, because
of the potential volumetric heat generation across such nanojunctions, the
circuit stability becomes often a major concern, which necessitates to study
the heat transport properties at the molecular-scale. Here we report the
thermoelectric behavior of various tr-nuclear metal-string complexes,
$[M-M-M](dpa)_4(NCS)_2$ for $M \in \{Cr,Ru\}$, bridging Au(111) nanowires as
nanoelectrodes. Based on our charge transport analysis from
\textit{first-principles}, we find that the dominant transmission peaks tend to
move away from the Fermi level upon systematic rutheniation in chromium-based
metal-string complexes due mainly to the coupling of $\pi^{*}$ orbitals from Ru
and $\sigma_{nb}$ orbitals from Cr. Such type of a metal-string junction can
also exhibit strong Coulomb interaction so that its thermoelectric behavior
begins to deviate from the Wiedemann-Franz law. Our results further suggest
that metal-string complexes can render better thermoelectric devices especially
at the molecular-scale with the thermopower as high as 172 $\mu V/K$ at 300 K.
Considering the contributions from both electrons and phonons, even a high
\textit{figure of merit} of $ZT \sim 2$ may be attained for Cr-Cr-Cr based
metal-string molecular junctions at room temperature. Resonant enhancement in
the thermoelectric efficiency appears to occur in such systems through
alteration of inter-dot electrostatic interactions, which can be controlled by
incorporating Cr and Ru atoms in such tri-nuclear metal-string complexes.
