  We discuss a 3D model describing the time evolution of nematic liquid
crystals in the framework of Landau-de Gennes theory, where the natural
physical constraints are enforced by a singular free energy bulk potential
proposed by J.M. Ball and A. Majumdar. The thermal effects are present through
the component of the free energy that accounts for intermolecular interactions.
The model is consistent with the general principle of thermodynamics and
mathematically tractable. We identify the a priori estimates for the associated
system of evolutionary partial differential equations and construct
global-in-time weak solutions for arbitrary physically relevant initial data.
