  We consider a flow of non-Newtonian incompressible heat conducting fluids
with dissipative heating. Such system can be obtained by scaling the classical
Navier--Stokes--Fourier problem. As one possible singular limit may be obtained
the so-called Oberbeck--Boussinesq system. However, this model is not suitable
for studying the systems with high temperature gradient. These systems are
described in much better way by completing the Oberbeck--Boussinesq system by
an additional dissipative heating. The satisfactory existence result for such
system was however not available. In this paper we show the large-data and the
long-time existence of dissipative and suitable weak solution. This is the
starting point for further analysis of the stability properties of such
problems.
