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We consider a multilayer hyperbolic-parabolic PDE system which constitutes acoupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which theboundary interface coupling between 3D fluid and 3D structure is realized via a2D elastic equation. Our main result here is one of strong decay for the givenmultilayered - heat system. That is, the solution to this composite PDE systemis stabilized asymptotically to the zero state.  Our proof of strong stability takes place in the "frequency domain" andultimately appeals to the pointwise resolvent condition introduced by Tomilov[45]. This very useful result, however, requires that the semigroup associatedwith our multilayered FSI system be completely non-unitary (c.n.u).Accordingly, we firstly establish that the semigroup $\{e^{\mathcal{A}t}\}_{t\geq 0}$ is indeed c.n.u., in part by invoking relatively recentresults of global uniqueness for overdetermined Lam\'e systems on nonsmoothdomains. Although the entire proof also requires higher regularity results forsome trace terms, this \textit{"resolvent criterion approach"} allows us toestablish a "classially soft" proof of strong decay. In particular, it avoidsthe sort of technical PDE multipliers invoked in [9].

A Resolvent Criterion Approach to Strong Decay of a Multilayered Lam\'e-Heat System