Natural convective heat transfer from heated thin two-sided horizontal plates occurs in a number of practical situations. There have been many studies, both experimental and numerical, on heat transfer rates in such situations. Most of these studies have considered only steady state heat transfer from surfaces. However, flow and heat transfer rate may vary with time and therefore there is an interest in exploring heat transfer rates in unsteady flows. In the present study, attention has been given to the unsteady flow, following the instantaneous heating of the plate surfaces. Circular and square shaped plates have been considered and the temperatures of the upper and lower plate surfaces were assumed to be isothermal after the heating. The main interest was to study the heat transfer rate variation with time and the time taken for the flow to reach steady state. It was assumed that the heat transfer rate from the plate surfaces was to air. It was also assumed that the flow remained laminar and that the fluid properties remained constant, except for the density change with temperature which gives rise to the buoyancy forces (i.e., the Boussinesq equation). The mean heat transfer rate obtained has been expressed in terms of Nusselt number based on the difference between the plate surface temperature and the temperature of the undisturbed air far from the plate and on a length scale that is equal to the diameter of the plate in the case of a circular plate and that is equal to the side length in the case of a square plate. Results have been obtained for Rayleigh numbers of from 10² to 10⁵ and dimensionless times of up to 0.25. The results obtained for the circular plate were found to be very nearly the same as those obtained for the square plate. Nusselt number variations with dimensionless time show that at the lower Rayleigh numbers considered, the Nusselt number drops steadily from the high initial values to the low constant steady state values whereas at the higher Rayleigh numbers, the Nusselt number first drops from the high initial values to a minimum value and then rises to the final steady state value. The variations of the dimensionless time to reach a steady state with Rayleigh number show that this dimensionless time is approximately constant at the lower Rayleigh numbers considered but decreases very significantly with increasing Rayleigh numbers at the higher Rayleigh number considered.