  We consider charge and thermal transport properties of magnetically active
paramagnetic molecular dimer. Generic properties for both transport quantities
are reduced currents in the ferro- and anti-ferromagnetic regimes compared to
the paramagnetic and efficient current blockade in the anti-ferromagnetic
regime. In contrast, while the charge current is about an order of magnitude
larger in the ferromagnetic regime, compared to the anti-ferromagnetic, the
thermal current is efficiently blockaded there as well. This disparate behavior
of the thermal current is attributed to current resonances in the ferromagnetic
regime which counteract the thermal flow. The temperature difference strongly
reduces the exchange interaction and tends to destroy the magnetic control of
the transport properties. The weakened exchange interaction opens up a
possibility to tune the system into thermal rectification, for both the charge
and thermal currents.
