  The archetypal two-impurity Kondo problem in a serially-coupled double
quantum dot is investigated in the presence of a thermal bias $\theta$. The
slave-boson formulation is employed to obtain the nonlinear thermal and
thermoelectrical responses. When the Kondo correlations prevail over the
antiferromagnetic coupling $J$ between dot spins we demonstrate that the setup
shows negative differential thermal conductance regions behaving as a thermal
diode. Besides, we report a sign reversal of the thermoelectric current
$I(\theta)$ controlled by $t/\Gamma$ ($t$ and $\Gamma$ denote the interdot
tunnel and reservoir-dot tunnel couplings, respectively) and $\theta$. All
these features are attributed to the fact that at large $\theta$, both
$Q(\theta)$ (heat current) and $I(\theta)$ are suppressed regardless the value
of $t/\Gamma$ because the double dot decouples at high thermal biases.
Eventually, and for a finite $J$, we investigate how the
Kondo-to-antiferromagnetic crossover is altered by $\theta$.
