In this paper, we have numerically investigated the unsteady flow of blood and heat transfer in the overlapping stenosed arterial segment in the presence of magnetic field. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been employed to solve the full Navier-Stokes equation along with the thermal energy equation using implicit finite difference method by developing well known Peaceman- Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to estimate the flow patterns in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. The impact of wall shear stress and the Nusselt number have been examined for the effect of initial stenosis on the overlapped one. The wall shear stress, Nusselt number and flow resistance increases with increasing magnetic field strength. However, wall shear stress and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength up to 8T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment in cancer therapy.