<p>Viscoelastic materials exhibit time-dependent creep and stress relaxation. However, classical integer-order models fail to capture long-term memory effects and finite-speed heat propagation, especially under transient thermal shocks or at small scales. To address these limitations, this paper proposes a fractional viscoelastic model that integrates three features: the incorporation of the Caputo–Fabrizio fractional derivative with a nonsingular exponential kernel into the Kelvin–Voigt formulation to represent ultra-slow relaxation and hereditary behavior; the adoption of the nonlocal dual-phase-lag heat-conduction theory to enforce finite thermal-wave speeds and spatial nonlocality; and the use of a spherical cavity in an infinite medium as a canonical benchmark for stress concentrations and thermal gradients. Analytical solutions for temperature, displacement, and stress fields are obtained using Laplace transforms and a verified numerical inversion method. Results yield three physical insights. First, the fractional order reduces wave amplitudes by 14–30% compared with integer-order models, quantifying the damping effect of memory dependence. Second, increasing the nonlocal length scale from 0 to 0.09 raises the near-cavity temperature by 26% while reducing peak compressive stresses by 15–34%, showing that nonlocal heat-flux interactions redistribute thermal energy to mitigate stress concentrations. Third, fractional models exhibit steeper spatial decay; for example, a 99.97% temperature reduction occurs between the cavity surface and a point at twice that distance, eliminating unphysical infinite-speed propagation. The model recovers classical thermoelasticity and integer-order viscoelasticity as limiting cases and is relevant to aerospace thermal shielding, microelectronics heat dissipation, and biomedical implants, providing a thermodynamically consistent foundation for next-generation viscoelastic material design applications.</p>