One of the most important factors influencing the quality of the weld created by the micro friction stir welding is the amount of heat generated during the welding operation. Due to the lack of proper mixing of materials at low temperatures, joints' quality decreases due to the formation of cold welds. Also, overheating takes the process out of solid-state welding, which prevents good joints. Finite element analysis of friction stir welding leads to a better understanding of the effect of different parameters on the process. With the results extracted from such analysis, some of the output can be predicted, such as heat distribution. In the present study, in order to perform finite element analysis of the micro friction stir welding of Al 1050 to pure copper, the coupled Eulerian-Lagrangian method in Abaqus software has been used. The results of finite element analysis showed that the heat distribution on the copper side is wider due to the higher heat transfer coefficient of copper than aluminum. The maximum temperature in the analysis was recorded in the weld line, which was 392°C. The heat generated during the welding process was measured at different points relative to the joint line, and appropriate matching was observed with a comparison of experiments and simulation results.