The numerical simulation of fracture contact poromechanics is essential to develop and improve subsurface engineering for CO2 sequestration, production of geo-energy resources, energy storage and waste water injection. However, accurately modeling this problem presents significant challenges due to the complex physics involved in strongly coupled thermoporomechanical processes and the frictional contact mechanics of fractures. A fully implicit time scheme is applied to solve the resulting mathematical model, necessitating the use of an iterative linear solver to run the model. The solver's efficiency primarily depends on a robust preconditioner, which is particularly challenging to develop because it must decouple the linearized energy, momentum, and mass balance subproblems. This decoupling is further complicated by the saddle-point structure of the matrix arising from the Augmented Lagrange formulation of contact mechanics. In this presentation, we introduce a preconditioner for the problem based on nested Schur complement approximations. We leverage the connection between preconditioners and sequential iterative schemes to derive efficient approximations of the Schur complements, enabling the decoupling of equations. Fixed stress-based stabilization terms are employed for the flow and energy equations. The stabilization coefficients are extended to account for the flow and energy both in the porous matrix and in fractures. This approach is combined with treatment of the saddle-point structure of the contact subproblem. The performance of the linear solver is investigated through numerical experiments with grid refinement and different physical regimes.