Cooling assisted friction stir welding (CFSW) suppresses formation of intermetallic compounds (IMCs) and improves tensile strength of the dissimilar joints. The present investigation provides a 3D finite element based mathematical model to predict the thermal gradient of CFSW considering a material flow pattern of dissimilar Al-Cu joint. A definite heat transfer mathematical model between tool and workpiece interaction and Gaussian based cooling sources is employed in simulation. A numerical methodology to present the material mixing at Al-Cu joint is proposed considering the experimental distribution of Al and Cu particles in stir zone using functionally graded material (FGM). The results obtained through this material and heat transfer model are validated by experiments of water CFSW for the temperature gradient. The proposed volume fraction of Cu particle in Al matrix inside the stir zone is found inline with the experimental results. Horizontal material movement from advancing side to retreating side and vertical material movement from top to bottom of the stir zone are also found close with simulated results. The robustness of the present numerical model is observed with better agreement to experimental results for peak temperatures through reliability analysis.