The free convection flow along a horizontal plate whose temperature oscillates about a non-zero mean is analysed. The basic flow is purely buoyancy induced while the oscillation in the plate temperature causes a time dependent boundary layer flow and heat transfer. Two separate solutions valid for high and low frequency ranges are developed. The velocity and temperature are obtained by a series expansion in terms of frequency parameters. For very high frequencies, the oscillatory flow pattern is of “Shear Wave” type unaffected by the mean flow and predicts a phase lead of π/4 in the local rate of heat transfer fluctuations while the skin friction has a phase lag of π/2.