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 $theta$.
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