  We report an experimental study aiming to clarify the role of boundary
conditions (BC) in high Rayleigh number $10^8 < {\rm{Ra}} < 3 \times 10^{12}$
turbulent thermal convection of cryogenic helium gas. We switch between BC
closer to constant heat flux (CF) and constant temperature (CT) applied to the
highly conducting bottom plate of the aspect ratio one cylindrical cell 30 cm
in size, leading to dramatic changes in the temperature probability density
function and in power spectral density of the temperature fluctuations measured
at the bottom plate, while the dynamic thermal behaviour of the top plate and
bulk convective flow remain unaffected. Within our experimental accuracy, we
find no appreciable changes in Reynolds number Re(Ra) scaling, in the
dimensionless heat transfer efficiency expressed via Nusselt number Nu(Ra)
scaling, nor in the rate of direction reversals of large scale circulation.
