This paper demonstrates the theoretical study of heat transfer over the wire coating process for the Carreau fluid. The process of coating wire or cables enhances the mechanical and electrical strength of the wire. The aim is to improve the understanding and control of the wire-coating process when using viscoelastic fluids, to optimize coating quality, uniformity, and efficiency, as well as to identify the most effective process parameters. First, we modeled the problem for cylindrical coordinates, and then the Flow governing equation are simplified using normalized variables and parameters. After making changes, we used the perturbation method to solve the final equation and obtain the analytical expression for the velocity distribution as well as the pertinent engineering quantities. Afterward, we used the Runge-Kutta fourth-order approach to solve it numerically. The velocity of molten polymer increases with increasing the values of We. The temperature profile increases with increasing the values of the pressure gradient parameter (A), (delta) and Brinkman number (Br). The effects of the We and pressure gradient are discussed with the help of various graphs. Hybrid nanofluids are versatile and have a wide range of potential applications due to their enhanced thermal, mechanical, and fluidic properties.