The free-standing thin films of melted poly(ethylene oxide) have been extensively simulated by the chemically specific coarse-grained (CG) molecular dynamics (MD) method. It is revealed that if the polymer thin film becomes thinner than some critical value, it would initially turn into a fiber, accompanied by an increase in the free surface area and a decrease in surface tension. A simple but efficient scheme is proposed to determine the critical interfacial thickness and the film thickness from the non-intrinsic density and pressure profiles, and the ratio of the two thicknesses is defined as the interfacial fraction. The critical film thickness is found to increase with the number of chains or equivalently the transverse area. With increasing temperature, the critical interfacial thickness increases a bit whereas the critical film thickness slightly decreases, highlighting the important role of the interfacial fraction. For both of the “critical” and “thick” films, the outermost surface layers are confirmed to undergo the greatest movements. The “critical” film exhibits the intrinsic interfacial thickness and bulk density almost identical to those of the “thick” film, dictating the thickness independence of the surface tension. Therefore, the phase stability of the film is essentially determined from the intrinsic thickness of the bulk layer, and the identified temperature dependence of the critical film thickness can be mainly explained by the surface tension.