  We propose a model for thermo-elastic beams, consistent with the theory of
linear three-dimensional thermo-elasticity and deduced by a suitable version of
the Principle of Virtual Powers. Dimensional reduction is achieved by
postulating convenient \textit{a priori} representations for mechanical and
thermal displacements, the latter playing the role of an additional kinetic
variable. Such representations are regarded as internal constraints, some
involving the first, others the second gradient of deformation and thermal
displacements; these constraints are maintained by reactive stresses and
hyper-stresses of the type occurring in non-simple elastic materials of grade
two, and by reactive entropy influxes and hyper-influxes.
