The design and operation of lab-on-a-chip systems that are based on electrical circuits require fluids that are propelled by thermo-electrokinetic forces. On-chip operations including the generation of heat along microchannels and the control of liquid flow are all relevant in the traditional sense. The influence of heat on pseudoplastic fluid flow is demonstrated in this work using electro-osmotic (EOF) peristaltic pumping. The fundamental heat-transport equations that govern microchannel applications are developed from theoretical considerations. Explicit equations are presented for pressure gradient, stream functions, heat transfer coefficient, and temperature distribution when long wavelength and low Reynolds numbers are taken into account. Analytical solutions employ a regular perturbation approach. Then, mathematica software is used to solve the resulting equation. Physical quantities are analyzed using a variety of parameters. The results are visibly presented for each parameter at the end.