The existence of proper weak solutions of the Dirichlet-Cauchy problem
constituted by the Navier-Stokes-Fourier system which characterizes the
incompressible homogeneous Newtonian fluids under thermal effects is studied.
We call proper weak solutions such weak solutions that verify some local energy
inequalities in analogy with the suitable weak solutions for the Navier-Stokes
equations. Finally, we deal with some regularity for the temperature.