A direct numerical simulation of thermal convection between horizontal plane boundaries has been performed, at a Rayleigh number Ra=9800 Rac, where Racis the critical Rayleigh number for the onset of convection (Pr=0.72). The flow is found to be fully turbulent and analysis of the probability distributions for temperature fluctuations indicates that this is within the ‘‘hard turbulence’’ regime, as defined by the Chicago group. Good agreement is shown to exist between their experiments and the present simulation.