We consider the mixed initial-boundary value problem in the context of the
Moore-Gibson-Thompson theory of thermoelasticity for dipolar bodies. We consider the case of heat conduction with dissipation. Even if the elasticity tensors
are not supposed to be positively defined, we have proven both, the uniqueness
and the instability of the solution of the mixed problem. In the case that the mass
density and the thermal conductivity tensor are positive, we obtain the uniqueness
of the solution using some Lagrange type identities.