  This paper is concerned with a non-isothermal Cahn-Hilliard model based on a
microforce balance. The model was derived by A. Miranville and G. Schimperna
starting from the two fundamental laws of Thermodynamics, following M. Gurtin's
two-scale approach. The main working assumptions are made on the behaviour of
the heat flux as the absolute temperature tends to zero and to infinity. A
suitable Ginzburg-Landau free energy is considered. Global-in-time existence
for the initial-boundary value problem associated to the entropy formulation
and, in a subcase, also to the weak formulation of the model is proved by
deriving suitable a priori estimates and showing weak sequential stability of
families of approximating solutions. At last, some highlights are given
regarding a possible approximation scheme compatible with the a-priori
estimates available for the system.
