  The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative
noise of transport type is studied in the $L^2$-setting. It is shown that,
under a suitable scaling of the noise, weak solutions to the stochastic 2D
Boussinesq equations converge weakly to the unique solution of the
deterministic viscous Boussinesq system. Consequently, the transport noise
asymptotically regularizes the inviscid 2D Boussinesq system and enhances
dissipation in the limit.
