This article describes the effect of thermal radiation on the non-Newtonian third grade fluid used as a coating material for wire coating analysis with temperature dependent viscosity. The basic governing equations of continuity, momentum and energy are incorporated. The effect of thermal radiation and viscous dissipation terms are included in the energy equation. The Reynolds and Vogel’s models have been considered for temperature dependent viscosity. The approximate solution is obtained by HAM (homotopy analysis method). The approximate solution is compared with the numerical solution obtained by ND-Solve method. The effect of different parameters involved in the solution such as non-Newtonian parameter β, Reynolds model viscosity parameter χ, Vogel’s model viscosity parameter Ω, thermal radiation parameter R and Brinkman number Br is discussed in detail. It is observed that the non-Newtonian property β of the fluid is favorable for increasing the velocity and temperature distribution. The magnetic parameter M increases the temperature. The viscosity parameters χ and Ω decrease the velocity of the fluid while the temperature profile increases. An increase in the thermal radiation parameter R and Brinkman number Br accelerate the velocity and temperature of the melt polymer so as to make the process faster.