  In the diffusive scaling and in the whole space, we prove the global
well-posedness of the scaled Boltzmann-Bose-Einstein (briefly, BBE) equation
with high temperature in the low regularity space $H^2_xL^2$. In particular, we
quantify the fluctuation around the Bose-Einstein equilibrium
$\mathcal{M}_{\lambda,T}(v)$ with respect to the parameters $\lambda$ and
temperature $T$. Furthermore, the estimate for the diffusively scaled BBE
equation is uniform to the Knudsen number $\epsilon$. As a consequence, we
rigorously justify the hydrodynamic limit to the incompressible
Navier-Stokes-Fourier equations. This is the first rigorous fluid limit result
for BBE.
