An analysis is performed to study the effects of unsteady incompressible flow past a vertical cone with variable surface temperature T-w'(x) = T-infinity' + ax(n) varying as a power function of distance from the apex (x = 0) and magnetic field applied normal to the surface. The dimensionless coupled partial differential boundary layer equations are solved numerically using an efficient and unconditionally stable finite-difference scheme of the Crank-Nicolson type. The velocity and temperature fields have been studied for various combinations of physical parameters (Prandtl number, Pr, exponent in power law variation in surface temperature, n, and magnetic field parameter, M). The local as well as average skin friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in the literature and are found to be in good agreement.