  The aim of this work is to examine the upper-semicontinuity properties of the
family of global attractors admitted by a non-isothermal viscous relaxation of
some nonlocal Cahn-Hilliard equations. We prove that the family of global
attractors is upper-semicontinuous as the perturbation parameters vanish.
Additionally, under suitable assumptions, we prove that the family of global
attractors satisfies a further upper-semicontinuity type estimate whereby the
difference between trajectories of the relaxation problem and the limit
isothermal non-viscous problem is explicitly controlled, in the topology of the
relaxation problem, in terms of the relaxation parameters.
