  Harnessing the abstract power of the celebrated result due to Borichev and
Tomilov (Math.\ Ann.\ 347:455--478, 2010, no.\ 2), we study the energy decay in
a one-dimensional coupled wave-heat-wave system. We obtain a sharp estimate for
the rate of energy decay of classical solutions by first proving a growth bound
for the resolvent of the semigroup generator and then applying the asymptotic
theory of $C_0$-semigroups. The present article can be naturally thought of as
an extension of a recent paper by Batty, Paunonen, and Seifert (J.\ Evol.\
Equ.\ 16:649--664, 2016) which studied a similar wave-heat system via the same
theoretical framework.
