The process of continental convergence between India and Eurasia has been postulated to be one in which the Indian crust is injecting into the Tibetan lower crust [W.‐L. Zhao and W.J. Morgan, this issue]. This scenario is studied with two‐dimensional steady state models with a temperature‐dependent viscosity. The effects of viscous heating are included in the governing equations; shear heating could play an important role in the process of Indian crustal injection. The spatially uniform uplift of the Tibetan Plateau is used as a constraint to define a maximum allowable vertical stress difference on the top of the Tibetan lower crust and to denote the related critical viscosity. When both viscous heating and temperature‐dependent viscosity are included, an average viscosity of the Tibetan lower crust as high as 1020 Pa s would still not be able to produce a noticeable stress difference. Numerical calculations reveal a negative feedback mechanism in the thermal structure: Initial high viscosity would cause a large increase in viscous dissipation and raise the temperatures, thus serving to decrease the viscosity of the Tibetan lower crust as the steady state is approached. This mechanism provides a favorable condition for the injection of relatively stiff Indian crust.