  We consider a kinetic model whose evolution is described by a Boltzmann-like
equation for the one-particle phase space distribution $f(x,v,t)$. There are
hard-sphere collisions between the particles as well as collisions with
randomly fixed scatterers. As a result, this evolution does not conserve
momentum but only mass and energy. We prove that the diffusively rescaled
$f^\varepsilon(x,v,t)=f(\varepsilon^{-1}x,v,\varepsilon^{-2}t)$, as
$\varepsilon\to 0$ tends to a Maxwellian $M_{\rho, 0, T}=\frac{\rho}{(2\pi
T)^{3/2}}\exp[{-\frac{|v|^2}{2T}}]$, where $\rho$ and $T$ are solutions of
coupled diffusion equations and estimate the error in $L^2_{x,v}$.
