The classical theory is incapable of explaining the size-dependent behavior of small-scale structures. This theory also fails to describe a linear response of electric polarization to the temperature gradient. The mentioned effects can be explained by the local gradient theory of electrothermoelasticity that alongside the mechanical, thermal, and electromagnetic processes considers the effect of the changes in material microstructure on the solid behavior. Within the local gradient theory, the above changes in the material microstructure are linked with the process of the local mass displacement. The basic equations of this theory were obtained earlier based on the continuum-thermodynamic approach. In this study, the variational approach for the formulation of linear boundary-value problems of the local gradient electrothermoelasticity is proposed. Using this approach, the fundamental equations and proper boundary conditions which describe the physical behavior of the linear continuum are derived. The usefulness of the proposed theory is verified based on two simple problems. Namely, the theory is used to study the response of the electric polarization of the isotropic layer to the temperature gradient and to investigate the coupled field in a simply-supported piezoelectric nanobeam subjected to the distributed uniform force. A generalized mathematical model of the Bernoulli–Euler electroelastic beam is formulated. It is shown that the resulting local gradient beam model can capture the size-depending behavior of the piezoelectric beam at the nanoscale. The results obtained in this study are general and can be useful for modeling new devices based on size, thermopolarization, and piezoelectric effects.