The starting and stopping processes play an important role in reduce friction and abrasion of a spiral groove dry gas seal. Thus, the startup and shutoff of the seal is investigated by a numerical approach. The computational procedure based on the material properties of rotational and stationary rings, interaction of micro asperity, and frictional heat-flow coupling is implemented to build a three-dimensional thermo-mechanical coupling model considering sliding friction within rough-rigid body. And then, the ANSYS software is used to simulate the friction heat and the stress variation of rough-rigid body based on the characteristics of nonlinear multiphysics. The results are presented, and it shows that the maximum contact temperature value of the roughened surface increases with increase in the sliding time and presents a little fluctuation, and the distribution of VonMises equivalent stress is extremely nonuniform and non-linear. What’s more, the stress component of maximum x-direction(σ _xx) isn’t appeared in the region of highest contact asperity. The results reveal that a tensile stress is existed along the thickness direction of three-dimensional rough solid and the region of tensile stress is enlarged slightly with the sliding time. According to above results, it can be shown that increase in temperature and fluctuation are attributed to thermal conduction caused, the change of stress is due to the elastic-plastic deformation of asperities. These results illustrate the potential of numerical simulation in prediction the temperature and stress of seal faces during the starting and stopping process and may help in the design and optimization of spiral groove dry gas seal.