This research object is focused to discuss the peristaltic motion in a horizontal channel. Non-Newtonian cross fluid model is considered in the analysis. Wall properties, viscous dissipation and MHD effects are also taken into account. Governed mathematical equations are solved by numerical method after using lubrication approximation. To see the theoretical consequence of peristaltic wave along channel, graphical results are plotted for different innovative parameters which are discussed in detail. Stream lines are strategized to see the circulation pattern in presence of considered effects. From a theoretical point of view, it is noted that peristaltic waves accelerate the fluid circulations more significantly near the walls. Moreover, the ambient temperature is shown to rise when the Brinkman number increases. Basically, higher values of Br correspond to stronger viscous dissipation, i.e., stronger heat generation due to friction is used by shear in the flow which raises the fluid temperature.