A Rayleigh-Bénard cell has been designed to explore the Prandtl (Pr) dependence of turbulent convection in the cross-over range 0.7 < P r < 21 and for the full range of soft and hard turbulences, up to Rayleigh number Ra ≃ 10 11 . The set-up benefits from the favourable characteristics of cryogenic helium-4 in fluid mechanics, in-situ fluid property measurements, and special care on thermometry and calorimetric instrumentation. The cell is cylindrical with diameter/height = 0.5. The effective heat transfer Nu(Ra, P r) has been measured with unprecedented accuracy for cryogenic turbulent convection experiments in this range of Rayleigh numbers. Spin-off of this study include improved fits of helium thermodynamics and viscosity properties. Three main results were found. First the Nu(Ra) dependence exhibits a bimodality of the flow with 4 − 7% difference in Nu for given Ra and P r. Second, a systematic study of the side-wall influence reveals a measurable effect on the heat transfer. Third, the Nu(P r) dependence is very small or null : the absolute value of the average logarithmic slope (dlnNu/dlnP r) Ra is smaller than 0.03 in our range of P r, which allows to disciminate between contradictory experiments [Ashkenazi et al., Phys. Rev.Lett. 83:3641 (1999)] [Ahlers et al., Phys.Rev.Lett. 86:3320 (2001)].