<p>This study examines the thermal and hydrodynamic behavior of Williamson non-Newtonian mucus in a two-dimensional divergent wavy microchannel, simulating ciliated surfaces with an eighth-order waveform. The flow is modeled as laminar, incompressible, and governed by low Reynolds number hydrodynamics, with equations transformed into a cilia-attached moving frame. Employing a long-wavelength approximation, inertia effects are neglected, and a perturbation method analyzes deviations from rheological and geometric nonlinearities. The interplay between shear-thinning effects, channel divergence, and undulation-driven periodicity is explored, with temperature distribution incorporating viscous dissipation and heat transfer. Graphical results illustrate velocity profiles, pressure gradients, streamline patterns, and thermal performance, highlighting how cilia motion enhances mixing and heat transfer in microfluidic systems. Crucially, divergence angle and Williamson rheology are shown to significantly alter flow structure, as evidenced by velocity vector fields. These findings provide critical insights for the design of bio-inspired microfluidic devices, particularly those requiring optimized thermal management and mixing.</p>