In this paper, we use the Green-Naghdi theory of thermomechanics of continua to derive a linear theory of thermopiezoelectricity of a body with inner structure. This theory permits propagation of thermal waves at finite speed. We establish a uniqueness result and a continuous dependence of the solutions upon initial data and body supplies. Some applications (the problem of a concentrated heat source, the problem of an impulsive body force, the deformation of a thick-walled spherical shell) are presented.