  This paper addresses a nonstationary flow of heat-conductive incompressible
Newtonian fluid with temperature-dependent viscosity coupled with linear heat
transfer with advection and a viscous heat source term, under Navier/Dirichlet
boundary conditions. The partial regularity for the velocity of the fluid is
proved to each proper weak solution, that is, for such weak solutions which
satisfy some local energy estimates in a similar way to the suitable weak
solutions of the Navier-Stokes system. Finally, we study the nature of the set
of points in space and time upon which proper weak solutions could be singular.
