Liquid metal (LM) breeder blanket is a topic of great interest in the fusion reactor blanket design because of many advantages. In the breeding blanket of the fusion reactor, the dynamic viscosity of LM is impacted by heat transfer, resulting in the change of velocity distribution. The influence of heat transfer on magnetohydrodynamic flow in a rectangular duct at high Hartmann number is investigated by a coupling method. By this method, the velocity field is calculated through a second-order projection method, coupled with the temperature distribution computed by a finite-volume method. The numerical result without temperature influence is validated by Hunt's and Shercliff's analytical solutions, which shows very good accuracy. On the basis of this numerical code, the velocity distribution of a Hunt's case with temperature influence is simulated. The simulation result indicates that the velocity field is different from the benchmark solution as the result of the heat transfer.