The pattern and style of mantle convection govern the thermal evolution, internal dynamics, and large scale surface deformation of the terrestrial planets. In order to characterize the nature of heat transport and convective behaviour at Rayleigh numbers, Ra, appropriate for planetary mantles, from less than 10^4 to more than 10^8, we perform a set of laboratory experiments. Convection is driven by a temperature gradient imposed between two rigid surfaces. As the Rayleigh number is increased, two transitions in convective behaviour occur. First we observe a change from steady to time-dependent convection at Ra ~ 10^5. A second transition occurs at higher Rayleigh numbers, Ra ~ 5x10^6, with large scale time-dependent flow being replaced by isolated rising and sinking plumes. Corresponding to the latter transition, heat transport scales with Ra^0.17 rather than the Ra^0.28 scaling found at lower Ra.