This study aims to investigate the effects of a non-singular fractional derivative on the thermomechanical responses of a one-dimensional thermoviscoelastic cylinder cavity problem. Using the Mittag-Leffler function as a relaxation function in mathematical models provides a more precise and comprehensive depiction of the behavior of thermo-viscoelastic materials. The boundary surfaces of the cylinder cavity are traction-free and associated with thermal shock. The analytical solution in the transformed domain is derived using a combination of direct approaches and Laplace transform techniques. We present a systematic study of traveling discontinuities in a hereditary thermoelastic space at different values of fractional order parameter α. The study shows that waves in this model travel with finite speeds. This aspect is new for fractional models. Finally, we have constructed a conclusion for a specific problem based on the numerical results and accompanying 3D graphics, as well as discussed, the effect of the deformation on the area of the cross-section of the cylinder cavity.