Published experiments on natural turbulent convection in cryogenic He-4 gas show contradictory results in the values of Rayleigh number higher than 10^(11). This paper describes a new helium cryostat with a cylindrical cell designed for the study of the dependence of the Nusselt number on the Rayleigh number (up to approximate to 10^(15)) in order to help resolve the existing controversy among published experimental results.