This paper investigates the spatial decay estimates for a coupled Moore-Gibson-Thompson (MGT) and Fourier heat system defined on a semi-infinite cylindrical domain in ${\mathbb{R}}^3$. Under homogeneous initial-boundary conditions and suitable decay assumptions at infinity, we derive a second-order differential inequality satisfied by the total energy functional. By transforming this inequality into a first-order form via operator factorization, we establish explicit exponential decay estimates of the energy along the axial direction. The result generalizes the classical Saint-Venant principle to higher-order coupled dissipative systems and provides a quantitative characterization of spatial decay for MGT-Fourier-type equations in unbounded domains. The findings contribute to the mathematical theory of thermoviscoelasticity and offer a foundation for further studies on structural stability and long-time behavior in such coupled systems.

This study investigates the spatial decay estimate for a coupled Moore-Gibson-Thompson (MGT)-Fourier system on a semi-infinite cylinder in ${\mathbb{R}}^2$. The system is comprised of a third-order MGT displacement equation and a parabolic heat equation with symmetric coupling. Using a weighted energy functional and an integral-differential inequality, we establish the exponential decay along the axial direction. This result offers a generalized Saint-Venant principle for coupled dissipative thermoviscoelastic models, thus extending the classical analysis to higher-order systems and advancing our understanding of MGT equations in an unbounded domain.