<p>This study presents a sophisticated thermoelastic model that integrates dual-phase-lag theory, memory-dependent kernel operators, and two distinct temperature fields—thermodynamic and conductive. The framework accounts for microstructural effects and temperature-dependent internal heat sources within a spherical cavity, modeled using a non-Fourier heat conduction approach grounded in energy conservation. The resulting system of coupled partial differential equations captures the evolution of thermal and mechanical fields under nonequilibrium conditions. Exact analytical solutions are obtained via Laplace transformations, and the Dubner–Abate technique is employed for accurate numerical inversion to recover time-domain behavior. The model offers enhanced physical realism compared to classical and fractional approaches, effectively representing the delayed and spatially distributed propagation of heat. Numerical simulations highlight the influence of kernel structure, hysteresis, and temperature discrepancy on stress and temperature profiles. These findings demonstrate the model’s predictive capability for advanced applications in microelectronics, nano-engineered materials, biomedical systems, and smart structures. An appendix detailing the numerical scheme is included to support reproducibility.</p>