  We study the asymptotic behaviour of solutions to a one-dimensional coupled
wave-heat system with Coleman-Gurtin thermal law. As our main results, we
represent the system as a feedback interconnection between the wave part and
the Coleman-Gurtin part and, using the asymptotic theory of $C_0$-semigroups,
we show that the associated semigroup in the history framework of Dafermos is
polynomially stable with optimal decay rate $t^{-2}$ as $t\to\infty$. In
particular, we obtain a sharp estimate for the rate of energy decay of
classical solutions to the problem.
