  In this paper, we prove the global existence of weak solutions to the
non-isothermal nematic liquid crystal system on $\mathbb T^2$, based on a new
approximate system which is different from the classical Ginzburg-Landau
approximation. Local energy inequalities are employed to recover the estimates
on the second order spacial derivatives of the director fields locally in time,
which cannot be derived from the basic energy balance. It is shown that these
weak solutions conserve the total energy and while the kinetic and potential
energies transfer to the heat energy precisely. Furthermore, it is also
established that these weak solutions have at most finite many singular times
at which the energy concentration occurs, and as a result, the temperature must
increase suddenly at each singular time on some part of $\mathbb T^2$.
