  We consider a non--homogeneous incompressible and heat conducting fluid
confined to a 3D domain perforated by tiny holes. The ratio of the diameter of
the holes and their mutual distance is critical, the former being equal to
$\epsilon^3$, the latter proportional to $\epsilon$, where $\epsilon$ is a
small parameter. We identify the asymptotic limit for $\epsilon \to 0$, in
which the momentum equation contains a friction term of Brinkman type
determined uniquely by the viscosity and geometric properties of the
perforation. Besides the inhomogeneity of the fluid, we allow the viscosity and
the heat conductivity coefficient to depend on the temperature, where the
latter is determined via the Fourier law with homogenized (oscillatory) heat
conductivity coefficient that is different for the fluid and the solid holes.
To the best of our knowledge, this is the first result in the critical case for
the inhomogenous heat--conducting fluid.
