Although it was demonstrated that discrete molecular levels determine the sign and magnitude of the thermoelectric effect in single-molecule junctions, full electrostatic control of these levels has not been achieved to date. Here, we show that graphene nanogaps combined with gold microheaters serve as a testbed for studying single-molecule thermoelectricity. Reduced screening of the gate electric field compared to conventional metal electrodes allows control of the position of the dominant transport orbital by hundreds of meV. We find that the power factor of graphene–fullerene junctions can be tuned over several orders of magnitude to a value close to the theoretical limit of an isolated Breit–Wigner resonance. Furthermore, our data suggest that the power factor of an isolated level is only given by the tunnel coupling to the leads and temperature. These results open up new avenues for exploring thermoelectricity and charge transport in individual molecules and highlight the importance of level alignment and coupling to the electrodes for optimum energy conversion in organic thermoelectric materials.