  We consider a nonlinear plate equation with thermal memory effects due to
non-Fourier heat flux laws. First we prove the existence and uniqueness of
global solutions as well as the existence of a global attractor. Then we use a
suitable Lojasiewicz--Simon type inequality to show the convergence of global
solutions to single steady states as time goes to infinity under the assumption
that the nonlinear term $f$ is real analytic. Moreover, we provide an estimate
on the convergence rate.
