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The poly ethylene terephthalate near the glass transition temperature highlights a strongly non linear elastic and viscous behaviour when biaxially stretched at high strain rates representative of the injection stretch blow moulding process. A non linear visco-hyperelastic model, where characteristics are coupled to the temperature, has already been identified from equi-biaxial tension experimental results. The weak form of the mechanical part of the model is presented and implemented into a finite element code developed in the Matlab environment and validated by comparing numerical simulation of equi-biaxial testing with the analytical solution in the isothermal case. Considering the thermal aspects, an experimental study, where PET sheets are heated using infrared (IR for short) lamps is also presented. The modeling of the IR radiation of the sheet helps to identify the thermal properties of the PET. The thermal model is then implemented in the finite element code, coupled to the 2D viscoelastic model. A discussion is made to justify the accuracy of the assumption made on homogeneity of the temperature field through the thickness. The simulation of the 2D plane stress equibiaxial test shows the important influence of the thermal aspects and the coupled thermo-mechanical software is used to quantify the self-heating phenomenon in the case of the biaxial elongations of PET sheets at high strain rates. POLYM. ENG. SCI., 53:2683–2695, 2013. © 2013 Society of Plastics Engineers