In this work, the finite element simulation of dissimilar friction stir welding process is investigated. The welded materials are AA 6061-T6 and AA 7075-T6 aluminum alloys. For this purpose, a 3D coupled thermo-mechanical finite element model is developed according to the Coupled Eulerian-Lagrangian (CEL) method. The CEL method has the advantages of both Lagrangian and Eulerian approaches, which means it can simultaneously solve the singularity in the large deformation problems and describe the physical boundary of the material accurately. In this paper, the effects of the position of the harder material (AA 7075-T6 aluminum alloy) and the tool pin profile on the temperature distribution and material flow in the weld metal and heat affected zone (HAZ) are investigated. The results show that the material velocity around the FSW tool is found to be higher using a grooved pin profile. Moreover, placing the harder material at the advancing side results in slightly lower process temperatures in comparison to the estimated temperature when the material is placed at the retreating side for all types of tool profiles. It has been proved that if the AA 7075-T6 aluminum alloy is at the advancing side, mixing happens in a thin layer below the tool shoulder, and the penetration of the harder material into the retreating side is found to be limited. In addition, good agreement between the temperature distribution obtained from the experimental measurements and numerical simulations is achieved and the accuracy of the numerical model is confirmed.