  The present work deals with the derivation of corrector estimates for the
two-scale homogenization of a thermo-diffusion model with weak thermal coupling
posed in a heterogeneous medium endowed with periodically arranged
high-contrast microstructures. The terminology "weak thermal coupling" refers
here to the variable scaling in terms of the small homogenization parameter of
the heat conduction-diffusion interaction terms, while the "high-contrast" is
thought particularly in terms of the heat conduction properties of the
composite material. As main target, we justify the first-order terms of the
multiscale asymptotic expansions in the presence of coupled fluxes, induced by
the joint contribution of Sorret and Dufour-like effects. The contrasting heat
conduction combined with cross coupling lead to the main mathematical
difficulty in the system. Our approach relies on the method of periodic
unfolding combined with a priori estimates for the thermal and concentration
fields and for their coupled fluxes.
