  In this paper we consider a family of three-dimensional problems in
thermoelasticity for linear elliptic membrane shells and study the asymptotic
behaviour of the solution when the thickness tends to zero.We fully
characterize with strong convergence results the limit as the unique solution
of a two-dimensional problem, where the reference domain is the common middle
surface of the family of three-dimensional shells. The problems are dynamic and
the constitutive thermoelastic law is given by the Duhamel-Neumann relation.
