<p>The mechanism of peristalsis with elastico-viscous fluids finds importance in physiological processes like analyzing blood circulation in arteries, designing peristaltic pumps for fluid movement in pipes for wastewater treatment, among others. The present work intends to investigate peristaltic activity through a curved channel containing an elastico-viscous fluid following the Walters-B model. This work stands out by examining viscoelastic effects in a curved channel while retaining the influence of inertial forces—an element often neglected in previous investigations. This research considers the combined effects of curvature, viscoelastic behavior, and thermal asymmetry, providing a more realistic picture of biological systems (like blood flow in arteries), where the outer wall (tissue side) is warmer due to body heat and the inner wall (lumen side) may have a different temperature due to flowing blood. The governing system is initially transformed into a dimensionless form in the wave frame and subsequently solved using a series solution approach, applicable for situations where the channel width is small relative to the wavelength of the peristaltic wave. In addition, thermal transport phenomena are formulated by incorporating viscous heating effects, which play a crucial role, particularly in peristaltic flow scenarios. The contributions of fluid elasticity and channel curvature on the axially induced motion, as well as on the heat transmission rates, are elucidated graphically. Key observations arising from the analysis of curved channels were found to be similar to those noted in earlier studies conducted under the lubrication approximation.</p>