  We investigate the heat flow between different terminals in an interacting
coherent conductor when inelastic scattering is present. We illustrate our
theory with a two-terminal quantum dot setup. Two types of heat asymmetries are
investigated: electric asymmetry $\Delta_E$, which describes deviations of the
heat current in a given contact when voltages are exchanged, and contact
asymmetry $\Delta_C$, which quantifies the difference between the power
measured in two distinct electrodes. In the linear regime, both asymmetries
agree and are proportional to the Seebeck coefficient, the latter following at
low temperature a Mott-type formula with a dot transmission renormalized by
inelasticity. Interestingly, in the nonlinear regime of transport we find
$\Delta_E\neq\Delta_C$ and this asymmetry departure depends on the applied bias
configuration. Our results may be important for the recent experiments by Lee
et al. [Nature (London) 498, 209 (2013)], where these asymmetries were
measured.
