The magnetohydrodynamic time-dependent von Karman swirling electrically conducting viscous fluid flow having a temperature-dependent viscosity due to a rotating disk impulsively set into motion is considered in this study. Alternative to the finite-difference methods frequently used to solve this flow, we propose here a better technique based on the spectral Chebyshev collocation in the direction normal to the disk and forward marching in time. When applied to the unsteady mhd flow in consideration, the devised numerical scheme is capable of generating the settlement of the flow into the well-known steady state for large times. The energy equation that incorporates the effects of viscous dissipation and Joule heating, and also coupled with the Navier-Stokes and continuity equations, is also treated by the method and the physical parameters of paramount interest as such the radial and tangential skin friction coefficients, the torque and the rate of heat transfer from the disk surface are numerically calculated that are shown to approach their steady state counterparts for the entire family of magnetic interaction and viscosity variation parameters. (C) 2009 Elsevier Masson SAS. All rights reserved.