Calculations of the radiative and phonon heat transfer between metals in an extreme near field in presence of electrostatic potential difference are given. Potential difference leads to a coupling between the radiation field and acoustic waves in solid, as a result of which the heat flux between two gold plates associated with p -polarized electromagnetic waves increases by many orders of magnitude as the potential difference varies from 0 to 10 V. The radiative heat transfer is compared with the phonon heat transfer associated with the electrostatic and van der Waals interactions between the surface displacements. For large potential difference and small distances the radiative heat transfer is reduced to the electrostatic phonon heat transfer. A particular case of surface acoustic waves-Rayleigh waves is studied in details. Conditions are obtained for the existence of surface phonon polaritons associated with the interaction of Rayleigh waves with an electromagnetic field. The surface Rayleigh and bulk acoustic waves can give contributions of the same order. The obtained results can be used to control heat fluxes at the nanoscale using the potential difference and to create coherent radiation sources based on the properties of the Rayleigh waves.