Fix rigid and Fix temp/berendsen, press/berendsen

Hi everybody,
I see the doc of the command Fix rigid: “You should not update the atoms in rigid bodies via other time-integration fixes (e.g. fix nve, fix nvt, fix npt)”.
But two Fix temp and press berendsen do not perform time integration. So, my first question is how about use fix rigid with berendsen thermo and barostat?
My second is can I consider a nanoparticle in a nanocomposite, with a diameter 3-7nm, so about 1000-10000 atoms, as a rigid body in a molecular dynamic simulation (maybe I lost some interaction between the particle and the matrix)?