  Fluid dynamics accompanies with the entropy production thus increases the
local temperature, which plays an important role in charged systems such as the
ion channel in biological environment and electrodiffusion in
capacitors/batteries. In this article, we propose a general framework to derive
the transport equations with heat flow through the Energetic Variational
Approach. According to thermodynamic first law, the total energy is conserved
and we can then use the Least Action Principle to derive the conservative
forces. From thermodynamic second law, the entropy increases and the
dissipative forces can be computed with the Maximum Dissipation Principle.
Combining these two laws, we then conclude with the force balance equations and
a temperature equation. To emphasis, our method provide a self consistent
procedure to obtain dynamical equations satisfying proper energy laws and it
not only works for the charge systems but also for general systems.
