An important problem arising in the cast film process is the so-called neck-in phenomenon, which may induce a drastic film width reduction as well as an inhomogeneous film thickness distribution (with the so called "dog-bone" defect on each side of the film). This neck-in phenomenon is highly influenced by the polymer rheology (increasing polymer elasticity leads to decrease markedly the neck-in), the stretching distance, the cooling conditions and the draw ratio. In this paper, we present a 2D Newtonian non-isothermal model based on a membrane approximation for the film. Stress balance, mass balance and temperature balance equations are solved iteratively using various finite element methods adapted to free surface problems and to transport equations. Coupling between mechanical and thermal equations is achieved introducing an Arrhenius temperature dependance for the viscosity. The influence of the heat transfer coefficient has been carefully investigated.