The thermal-mechanical coupling finite element method (FEM) was used to simulate a non-isothermal sheet metal extrusion process. On the basis of the finite plasticity consistent with multiplicative decomposition of the deformation gradient, the enhanced assumed strain (EAS) FEM was applied to carry out the numerical simulation. In order to make the computation reliable and avoid hourglass mode in the EAS element under large compressive strains, an alterative form of the original enhanced deformation gradient was employed. In addition, reduced factors were used in the computation of the element local internal parameters and the enhanced part of elemental stiffness. Numerical results show that the hourglass can be avoided in compression region. In the thermal phase, the boundary energy dissipation due to heat convection was taken into account. As an example, a circular steel plate protruded by cylindrical punch was simulated. The step-wise decoupled strategy is adopted to handle coupling between mechanical The thermal-mechanical coupling finite element method (FEM) was used to simulate a non-isothermal sheet metal extrusion process. On the basis of the finite plasticity consistent with multiplicative decomposition of the deformation gradient, the enhanced assumed strain (EAS) FEM was applied In order to make the computation reliable and avoid hourglass mode in the EAS element under large compressive strain, an alterative form of the original enhanced deformation gradient was employed. In addition, reduced factors were used in the computation of the element local internal parameters and the enhanced part of elemental stiffness. Numerical results show that the hourglass can be avoided in compression region. In the thermal phase, the boundary energy dissipation due to heat convection was taken into account. As an example, a circular steel plate protruded by cylindrical punch was simulated. The step-wise decoupled strategy was adopted to handle coupling between mechanical