Using recent results in the theory of C0-semigroups due to Batty et al. (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 et al. (2016) , which studied a similar wave-heat system with finite wave and heat parts using a celebrated result due to Borichev and Tomilov.