Viscoelastic behavior of Polyethylene Terephthalate (PET) is strongly dependent on the microstructure, and reciprocally, the microstructure evolution depends on the mechanical stresses [1]. Especially crystalline ratio and molecular orientation are characteristics of the microstructure evolution that change during the mechanical behavior of PET and/or with thermal conditions [2]. We are interested to model these phenomena at the mesoscopic scale by using the phase field method [3]. A numerical simulation coupled between microstructure and thermo-mechanical has been implemented and will help to build a viscoelastic model for PET at the macroscopic scale. We present here the first results that concerns crystallization under thermal conditions with no strain our stress effects. Using a phase field variable and a corresponding governing equation to describe the state (solid or liquid) in a material as a function of space and time, using also the thermal equations for heat, the problem can be solved without tracking the liquid-solid interface. The interfacial regions between liquid and solid involve smooth but highly localized variations of the phase-field variable. Three different method of numerical simulation (Finite volume method, Finite difference method and Finite element method) have been applied to our problem.