  We consider a non-Newtonian incompressible heat conducting fluid with
prescribed nonuniform temperature on the boundary and with the no-slip boundary
conditions for the velocity. We assume no external body forces. For the
power-law like models with the power law index bigger than $11/5$ in three
dimensions, we identify a class of solutions fulfilling the entropy equality
and converging to the equilibria exponentially in a proper metric. In fact, we
show the existence of a Lyapunov functional for the problem. Consequently, the
steady solution is nonlinearly stable and attracts all suitable weak solutions.
