Wellbore stability is a key to have a successful drilling operation. Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations. These stresses are significantly impacted by pore pressure variation and thermal stresses in the field. In order to address wellbore instability problems, it is important to investigate the mechanisms of rock–fluid interaction with respect to thermal and mechanical aspects. In order to understand the induced stresses, different mathematical models have been developed. In this study, the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically in Laplace domain. The results are transferred to time domain using Fourier inverse method. Finite difference method is also utilized to validate the results. Pore pressure and temperature distributions around the wellbore have been focused and simulated. Next, induced radial and tangential stresses for different cases of cooling and heating of formation are compared. In addition, the differences between thermo-poroelastic and poroelastic models in situation of permeable and impermeable wellbores are described. It is observed that cooling and pore pressure distribution reinforce the induced radial stress. Whereas cooling can be a tool to control and reduce tangential stress induced due to invasion of drilling fluid. In the next step, safe mud window is obtained using Mohr-Coulomb, Mogi-Coulomb, and modified Lade failure criteria for different inclinations. Temperature and pore pressure distributions do not change the minimum allowable wellbore pressure significantly. However, upper limit of mud window is sensitive to induced stresses and it seems vital to consider changes in temperature and pore pressure to avoid any failures. The widest and narrowest mud windows are proposed by modified Lade and Mohr-Coulomb failure criteria, respectively.