Most of the pore-scale imaging and simulations of non-Newtonian fluid are based on the simplifying geometry of network modeling and overlook the fluid rheology and heat transfer. In the present paper, we developed a non-isothermal and non-Newtonian numerical model of the flow properties at pore-scale by direct simulation of the 3D micro-CT images using a Finite Volume Method (FVM). The numerical model is based on the resolution of the momentum and energy conservation equations. Owing to an adaptive meshing technique and appropriate boundary conditions, rock permeability and mobility are accurately computed. A temperature and concentration-dependent power-law viscosity model in line with the experimental measurement of the fluid rheology is adopted. The model is first applied at isothermal condition to 2 benchmark samples, namely Fontainebleau sandstone and Grosmont carbonate, and is found to be in good agreement with the Lattice Boltzmann method (LBM). Finally, at non-isothermal conditions, an effective mobility is introduced that enables to perform a numerical sensitivity study to fluid rheology, heat transfer, and operating conditions. While the mobility seems to evolve linearly with polymer concentration, the effect of the temperature seems negligible by comparison. However, a sharp contrast is found between carbonate and sandstone under the effect of a constant temperature gradient. Besides concerning the flow index and consistency factor, a good master curve is derived when normalizing the mobility for both the carbonate and the sandstone.