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We calculate heat transfer between a 2D sheet (e.g. graphene) and a dielectric in presence of the gate voltage. The gate potential induces surface charge densities on the sheet and dielectric which results in coupling between an electric field and the surface displacements and, as a consequence, to an additional contributions to the radiative heat transfer. The electrostatic and van der Waals interactions between the surface displacement result in the phonon heat transfer which we calculate taking into account the nonlocality of these interactions. The nume