A novel approach is developed to represent coupled thermal-hydraulic-mechanical (THM) behavior of porous systems that incorporates the non-isothermal free and forced convection of a single component fluid in a non-boiling thermoelastic medium. The three-way simultaneous coupling between the THM triplet is currently linear, but no restriction is placed on incorporating material nonlinearities. The coupled PDEs are solved in space by grid-adaptive finite elements. The model is validated against solutions for linear non-isothermal consolidation of a column. We demonstrate the utility of the model by analyzing the behavior of a deep wellbore in a themoelastic medium circulated by a pressurized, but chilled fluid. Model results illustrate the significant importance of the cross-couplings between individual THM processes for the evaluation of wellbore stability.