Abstarct: Thermal Saffman-Taylor instability is a type of instability in a porous medium that occurs at the interface between two moving fluids that differ in temperature and viscosity. This phenomenon has attracted the attention of many researchers due to its occurrence during secondary oil recovery. Most previous studies have been performed on this instability in the Hell-Shaw cell for Newtonian fluids. In the present study, this instability was investigated in a porous medium for a hot non-Newtonian displacing fluid and a cold Newtonian displaced fluid. The use of non-Newtonian fluids and polymeric materials helps to increase the recovery of oil. Viscosity ratio, non-Newtonian fluid characteristics such as time constant, power index, temperature dependence and environmental anisotropy affect the viscous thermal finger instability that will be investigated in this study. In isothermal flows in Newtonian fluids, changes in viscosity are due to changes in the concentration of chemical components in the fluid, but in non-isothermal flows, changes in viscosity are due to changes in temperature and concentration. In non-Newtonian fluids, this parameter depends also on the shear rate. The dependence of viscosity on temperature and shear rate makes some differences between isothermal and non-isothermal flows in Newtonian and non-Newtonian fluids. The present problem is baxsed on miscible displacements and the non-Newtonian fluid is an independent of time fluid, so the Carreau-Yasuda model is used. The results show that by increasing time constant of the dicplacing fluid, the flow will be canalized and the sweep efficiency decrease. When the flow is canalized, the displacing fluid leaves from the generated channel and has no tendency to move the second fluid. This will not happen in the flow of two Newtonian fluids. Examination of the non-Newtonian fluid power index shows that in very small values of this number, the flow is more stable and the mixing length diagrams have lower oscillations. Non-Newtonian fluids with smaller power indices produce a more stable flow. The results show that high temperature reduces the viscosity of fluids, which is more intense in the second fluid due to its higher viscosity, and as a result, the mobility ratio decreases and the intensity of finger growth decreases. As a result, the sweep efficiency increases and the mixing length decreases. At lower Brinkman numbers, the temperature decreases later and resulting more stable flow. Examining Pecklet number shows that by decreasing this number, the penetration power of the fluid in the environment increases, as a result of which the boundary area between the two fluids expands and the two fluids are more distributed in each other; Therefore, the fingers will reach the end border of the geometry later and the flow will be more stable. The results of the study of instability in an anisotropic porous medium indicate that by increasing the permeability of the medium and mass in the direction of flow to permeability in the direction perpendicular to the flow, the instability decreases and a more stable flow is obtained. Increasing the anisotropy angles also contributes to the instability of the flow.