A reservoir-geomechanics coupled simulation tool is required in the interpretation and prediction of stimulation and production performance of unconventional reservoirs in a physically rigorous manner. One such a coupled simulation tool developed at Lawrence Berkeley National Laboratory (LBNL), TOUGH2-FLAC3D, has been extensively adopted in many scientific research and practical application projects in last two decades. In TOUGH2's most often used equation of state (EOS), EOS4, the vapor pressure is used as a primary variable, however, the vapor pressure lowering effect is not the primary interest in a typical reservoir flow simulation. Instead, the temperature should be a natural and physically correct primary variable, considering the convenience of model input, and the understanding and interpretation of simulation results. In this work, the vapor pressure is replaced by temperature in the EOS implementation. To be consistent with the change of primary variable, the Jacobian matrix is modified correspondingly and illustrated using a case of two-phase flow in one grid block. The development work was verified in three well-defined problems that are related to fluid diffusion, thermal conduction, thermal fluid conduction and convection, respectively, through comparing the modeling results with the corresponding analytical solutions.