  We investigate finite amplitude stability of spatially inhomogeneous steady
state of an incompressible viscoelastic fluid which occupies a mechanically
isolated vessel with walls kept at spatially non-uniform temperature. For a
wide class of incompressible viscoelastic models including the Oldroyd-B model,
the Giesekus model, the FENE-P model, the Johnson--Segalman model, and the
Phan--Thien--Tanner model we prove that the steady state is stable subject to
any finite perturbation.
