  We study heat rectification through quantum dots in the Coulomb blockade
regime using a master equation approach. We consider both cases of two-terminal
and four-terminal devices. In the two-terminal configuration, we analyze the
case of a single quantum dot with either a doubly-degenerate level or two
non-degenerate levels. In the sequential tunneling regime we analyze the
behaviour of heat currents and rectification as functions of the position of
the energy levels and of the temperature bias. In particular, we derive an
upper bound for rectification in the closed-circuit setup with the
doubly-degenerate level. We also prove the absence of a bound for the case of
two non-degenerate levels and identify the ideal system parameters to achieve
nearly perfect rectification. The second part of the paper deals with the
effect of second-order cotunneling contributions, including both elastic and
inelastic processes. In all cases we find that there exists ranges of values of
parameters (such as the levels' position) where rectification is enhanced by
cotunneling. In particular, in the doubly-degenerate level case we find that
cotunneling corrections can enhance rectification when they reduce the
magnitude of the heat currents. For the four-terminal configuration, we analyze
the non-local situation of two Coulomb-coupled quantum dots, each connected to
two terminals: the temperature bias is applied to the two terminals connected
to one quantum dot, while the heat currents of interest are the ones flowing in
the other quantum dot. Remarkably, in this situation we find that non-local
rectification can be perfect as a consequence of the fact that the heat
currents vanish for properly tuned parameters.
