The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.