  Thermal transport through a Coulomb-blockade quantum dot (QD) coupled to two
metallic leads is studied using five different approaches to the master
equation in which sequential and coutuneling terms are taken into account. In
the presence of intradot Coulomb interactions, a plateau in the
thermo-particle, the heat, and the energy currents is seen. The current plateau
diminishes at a high thermal bias between the leads. It is shown that the
Pauli, the Redfield, the Lindblad-type equation with first order tunneling
rates, and first-order von-Neumann master equations give very similar thermal
transport indicating the conservation of coherency in the electron transport in
sequential tunneling between the QD and leads. In contrast, the thermal
transport is suppressed when coutuneling processes are taken into account via a
second-order von-Neumann master equation. The consideration of second order
effects with respect to the QD-leads coupling brings in a wealth of virtual
processes at the contact to each lead. These virtual processes directly weaken
the effects of the contribution of the first order direct processes to the
overall transport, and introduce important other aspects of the transport, as
level broadening, energy shifts, and lifetimes in the time-domain. As a result
the current plateau formed via the Coulomb interaction diminishes, when second
order and cotunneling processes are considered.
