  In this paper, we use the Green-Naghdi theory of thermomechanics of continua
to derive a nonlinear theory of thermoelasticity with microtemperatures of type
III. This theory permits propagation of both thermal and microtemperatures
waves at finite speeds with dissipation of energy. The equations of the linear
theory are also obtained. With the help of the semigroup theory of linear
operators we establish that the linear anisotropic problem is well posed and we
study the asymptotic behavior of the solutions. Finally, we investigate the
impossibility of the localization in time of solutions.
