<p>This study presents a novel thermoelasticity framework that extends classical elasticity theory by integrating spatial and temporal nonlocality through a Klein–Gordon-type isotropic elasticity model. The proposed approach incorporates internal length and time scales alongside conventional thermoelastic properties to more accurately capture the dynamic behavior of nanostructures. Thermal diffusion is modeled using the dual-phase-lag (DPL) heat transfer theory, while nonlocal constitutive relations are developed with a dynamic kernel function to account for nonlocal interactions. The model analyzes transverse vibrations of axially moving Euler–Bernoulli (EB) thermoelastic nanobeams subjected to axial forces and external excitations. Numerical simulations and parametric studies reveal the significant influence of axial velocity, nonlocal effects, phase-lag parameters, and external loads on vibrational response. The findings highlight the critical role of nonlocal parameters in governing system stability and performance, offering valuable insights for designing advanced nanostructures in dynamic environments.</p>