Active control over the flow of heat in the near-field holds promise for nanoscale thermal management, with applications in refrigeration, thermophotovoltaics, and thermal circuitry. Analogously to its electronic counterpart, the metal-oxide-semiconductor (MOS) capacitor, we propose a thermal switching mechanism based on accumulation and depletion of charge carriers in an ultra-thin plasmonic film, via application of external bias. In our proposed configuration, the plasmonic film is placed on top of a polaritonic dielectric material that provides a surface phonon polariton (SPhP) thermal channel, while also ensuring electrical insulation for application of large electric fields. The variation of carrier density in the plasmonic film enables the control of the surface plasmon polariton (SPP) thermal channel. We show that the interaction of the SPP with the SPhP significantly enhances the net heat transfer. We study SiC as the oxide and explore three classes of gate-tunable plasmonic materials: transparent conductive oxides, doped semiconductors, and graphene, and theoretically predict contrast ratios as high as 225%.