  Using recent results in the theory of $C_0$-semigroups due to Batty, Chill
and Tomilov (J. Eur. Math. Soc. 18(4):853-929, 2016) we study energy decay in a
one-dimensional coupled wave-heat system with finite wave part and infinite
heat part. Our main result provides a sharp estimate for the rate of energy
decay of a certain class of classical solutions. The present paper can be
thought of as a natural sequel to a recent work by Batty, Paunonen and Seifert
(J. Evol. Equ. 16:649-664, 2016), which studied a similar wave-heat system with
finite wave and heat parts using a celebrated result due to Borichev and
Tomilov.
