  We investigate thermal transport in a serial asymmetric double quantum dot
(DQD) coupled to two electron reservoirs with different temperatures. The
inter- and intra-Coulomb interactions are taken into account in a Coulomb
blockade DQD where the electron sequential tunneling via four different master
equation approaches is considered. In the absence of Coulomb interactions, a
neglectable thermoelectric and heat currents is found identifying as the
Coulomb blockade DQD regime. In the presence of Coulomb interactions, intra-
and inter-Coulomb interactions, crossings energies between the intra- and the
inter-dot many-body electron states are observed. The crossings induce extra
channels in the energy spectrum of the DQD that enhance thermoelectric and heat
currents. The extra channels form several peaks in the thermoelectric and heat
currents in which intensity and position of the peaks depend on strength of the
inter- and intra-dot Coulomb interactions. In addition, the problem of
coherences and incoherences are studied using different approaches to the
master equation, which are the first order von-Neumann, the Redfield, a first
order Lindblad, and the Pauli methods. We find that all methods give almost
similar thermal transport when the role of the coherences is irrelevant in the
DQD.
