The paper considers a problem in which a steady-state sonic wave is propagated in the Longitudinal direction in a fluid enclosed between two horizontal parallel plates which are kept at different temperatures. The distance between the plates is much smaller than the sound wavelength. Rayleigh’s vortical acoustic streaming that appears in the region between the plates as a result of the sound wave leads to forced heat convection. The effect of that forced convection on heat transferred between the plates is analyzed theoretically. An acoustic Peclet number, which represents the interaction between heat conduction and forced convection is introduced, and asymptotic relations expressing the mean Nusselt number in terms of this dimensionless group are derived. The results obtained demonstrate that acoustic streaming results in a marked enhancement of heat transfer between the plates.