The effects of thermal radiation and viscous dissipation on the boundary layer flow of an electrically conducting non-Newtonian power-law fluids along a non-isothermal wedge in the presence of a transverse magnetic field are investigated. The resulting governing equations are transformed to a system of non-linear ordinary differential equations by using similarity transformation which is solved numerically by using fourth-order Runge-Kutta method with the shooting technique. Numerical results are given for the dimensionless velocity and the dimensionless temperature for various values of the magnetic parameter, the thermal radiation parameter and the Eckert number. Finally, numerical values of physical quantities such as the local skin-friction coefficient and the local Nusselt number are presented and discussed.