<p>A comprehensive theoretical investigation is carried out to analyse the peristaltic transport of a viscous, incompressible, Jeffrey non-Newtonian fluid within an inclined, non-uniform channel. The analysis incorporates the complex influences of surface roughness and complete slip boundary conditions under electro-osmotic effects along with temperature-dependent viscosity and thermal conductivity. The fundamental conservation laws such as conservation of mass, momentum, and energy are applied to develop a mathematical model of the problem. The formulated governing equations are simplified under long-wavelength, low-Reynolds-number regime, and the electrostatic potential is simplified using the Debye–Huckel linearisation. The resulting system is solved using a perturbation technique. The formulation captures the coupled interaction between electrokinetic forces, thermal variations, and complex boundary effects governing microscale transport phenomena. The analysis reveals that electro-osmotic forcing and wall roughness significantly modulate velocity, temperature, concentration, and streamline structures, while temperature-dependent properties significantly influence thermal transport behaviour. A comparative assessment demonstrates marked deviations between Newtonian and non-Newtonian flow characteristics. The findings provide useful insights for the design and optimisation of advanced biomedical devices such as micro-pumps, drug-eluting stents, and laboratory-on-chip platforms that achieve controlled, targeted, and efficient drug delivery.</p>