We present a family of multi-stage preconditioners for coupled thermal-compositional problems. For thermal simulations, inadequate treatment of the energy equation can cause severe convergence degradation in the iterative solvers. We use Schur-complement decompositions to extract a temperature subsystem and improve the treatment of the energy equation. We show improved performance and robustness across different thermal regimes. The number of iterations is reduced by 40-85% compared to standard CPR, and the new methods exhibit almost no sensitivity to the thermal regime.