Flow patterns and heat transfer in a square cavity with perfectly conducting horizontal walls are described by direct simulation for Rayleigh numbers of 10(6)-10(9). The code uses second order time and space discretisations and non-uniform grids. For Ra = 10(6) or less a steady final state is found. Periodic characteristics are obtained at Ra = 10(7), and non periodic behaviour is found at higher Ra. Time averaged wall and mid plane Nusselt numbers (not previously known for this case) are reported and correlated. Their oscillation frequencies are determined to characterize the regime. The mid plane Nusselt number, (Nu) over bar (mid), always exceeds wall Nusselt numbers. (Nu) over bar (mid) represents the total heat moved by the cavity under the perfectly conducting condition. At Rayleigh numbers from 10(8) onwards, (Nu) over bar (mid) exceeds the corresponding value for the adiabatic problem.