  In this paper, we consider a non-isothermal electrokinetic model, which is
derived from the Energetic Variational Approach. The charge transport is
described through the Poisson-Nernst-Planck equations with variable
temperature, and the heat flux satisfies the Fourier's law. This
Poisson-Nernst-Planck-Fourier model satisfies both the first law and second law
of thermodynamics as well as the Onsager's reciprocal relations, thus it is
thermodynamic-consistent. Finally, we prove the global well-posedness for this
model under the smallness assumption of the initial data by the energy method.
