  We introduce a system of equations
  that models a non-isothermal magnetoviscoelastic fluid. We show that the
model is thermodynamically consistent,
  and that the critical points of the entropy functional with prescribed energy
correspond exactly with the equilibria of the system.
  The system is investigated in the framework of quasilinear parabolic systems
and shown to be
  locally well-posed in an $L_p$-setting. Furthermore, we prove that
  constant equilibria are normally stable. In particular, we show that
solutions
  that start close to a constant equilibrium exist globally and converge
exponentially fast to a (possibly different)
  constant equilibrium. Finally, we establish that the negative entropy serves
as a strict Lyapunov functional
  and we then show that every solution that is eventually bounded in the
topology of the natural state
  space exists globally and converges to the set of equilibria.
