Abstract: Focusing on the viscous incompressible magnetic fluid past a stretching impermeable sheet with lower temperature, the laminar flow and the heat transfer in its boundary layer caused by the tensile deformation of the plate were studied under a steady magnetic field. Dimension reducing and dimensionless processing of the original control equations were first carried out based on similarity principle, and then the equations were solved by a spectral method. Assuming that the fluid viscosity varied linearly with temperature, with the constant boundary conditions of flow and temperature fields, the effects were analyzed of the parameters of variable fluid viscosity, the electromagnetic parameters, and the Prandtl number on the flow and temperature fields. Compared with the classical fourth-order Runge-Kutta method, the spectral method is superior in stability and exponential convergence.