An electrically insulating layer of a dielectric liquid confined between horizontal conducting electrodes, the upper of which is warmer, becomes unstable with respect to the onset of steady convection when the voltage between the plates reaches a critical value. In a rapidly varying ac field this instability is due to the Kelvin body force which depends on the polarization P and the gradient of the electric field E. The present authors in a recent linear stability analysis [Chem. Phys. Lett. 179, 311 (1991)] for the critical voltage showed that as the gravitational Rayleigh number becomes increasingly negative the critical wave number at the onset of convection becomes very large. Now this analysis is extended to examine how the Nusselt number depends on the extent of supercriticality in the weakly nonlinear regime. As the temperature drop between the plates increases the fraction of the heat transfer associated with convection is found to pass through a maximum value when the critical horizontal wave number is close to 4 times its value when gravity is absent.