  We prove stochastic stability of the three-dimensional Rayleigh-B\'enard
convection in the infinite Prandtl number regime for any pair of temperatures
maintained on the top and the bottom. Assuming that the non-degenerate random
perturbation acts in a thin layer adjacent to the bottom of the domain, we
prove that the random flow periodic in the two infinite directions stabilises
to a unique stationary measure, provided that there is at least one point
accessible from any initial state. We also prove that the latter property is
satisfied if the amplitude of the noise is sufficiently large.
