​An analytical framework for time-fractional magneto-thermoelasticity in unbounded domains, focusing on heat conduction in materials exhibiting non-classical thermal behavior, are presented. Thermal transport is strongly influenced by temperature and the internal structure of the medium; in the presence of imperfections such as inclusions, voids, or microstructural defects, the heat transfer process often deviates from conventional diffusion laws. To model these complex phenomena, fractional calculus is employed, and the governing equations are reformulated using dimensionless variables. Analytical solution in the Laplace–Fourier domain was derived, with temperature distribution expressed in terms of Mittag-Leffler and Fox H-functions. The use of uncoupled thermoelastic theory allows for a simplified treatment by decoupling thermal and mechanical fields. Finally, numerical inversion techniques are used to reconstruct time-domain solutions for displacement and stress, demonstrating how fractional-order parameters influence both thermal wave propagation and material response.