Energy can be transferred in a radiative manner between objects with different electrical fluctuations. In this work, we consider near-field energy transfer between two separated parallel plates: one is graphene-covered boron nitride and the other a magneto-optic medium. We first study the energy transfer between the two plates having the same temperature. An electric current through the graphene gives rise to nonequilibrium fluctuations and induces the energy transfer. Both the magnitude and direction of the energy flux can be controlled by the electric current and an in-plane magnetic field in the magneto-optic medium. This is due to the interplay between nonreciprocal effective photonic temperature in graphene and nonreciprocal surface modes in the magneto-optic plate. Furthermore, we report that a tunable thermoelectric current can be generated in the graphene in the presence of a temperature difference between the two plates.