  Our purpose is to show the existence of weak solutions for unsteady flow of
non-Newtonian incompressible nonhomogeneous, heat-conducting fluids with
generalised form of the stress tensor without any restriction on its upper
growth. Motivated by fluids of nonstandard rheology we focus on the general
form of growth conditions for the stress tensor which makes anisotropic
Musielak-Orlicz spaces a suitable function space for the considered problem. We
do not assume any smallness condition on initial data in order to obtain
long-time existence. Within the proof we use monotonicity methods, integration
by parts adapted to nonreflexive spaces and Young measure techniques
