In simulations of contact/impact phenomena using finite element techniques, spurious oscillations and/or numerical instabilities continue to pose considerable difficulty for many analysts. Recently, the combination of thermodynamically based stability estimates and energy-momentum numerical approaches has proven to be useful in developing effective, unconditionally stable algorithms for mechanical contact/impact in the fully nonlinear regime. In this paper, these ideas are extended to coupled interface problems, by developing a new a priori stability estimate lbr the fully coupled thermomechanical contact problem in large deformations. The model framework encompasses inelastic heating and thermal softening within the contacting bodies, as well as frictional heating and thermal softening of the coefficient of friction on sliding interfaces. Also incorporated are pressure dependent heat transfer across these interfaces, and a fully coupled treatment of the conductive heat transfer occurring within the bodies. Use of the stability estimate to extend energy-momentum approaches to dissipative and thermally coupled phenomena is discussed, as is the development of an unconditionally stable adiabatic split of the coupled problem. The latter is shown to be useful in developing partitioned integration schemes for the coupled equations of evolution.