  Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by
random noise was established recently in Hofmanov$\acute{\mathrm{a}}$ et al.
(2019, arXiv:1912.11841 [math.PR]). The purpose of this work is to prove
non-uniqueness in law for the Boussinesq system forced by random noise.
Diffusion within the equation of its temperature scalar field has a full
Laplacian and the temperature scalar field can be initially smooth.
