The present article investigates MHD-mixed convection heat transfer about a thin vertical plate in the presence of viscous dissipation and wall conduction (i.e. conjugate) heat transfer effects. The fluid is assumed to be incompressible and dense. The Keller box method, an implicit finite difference method, is used in the solution of the nonlinear boundary layer equations, following their transformation into the non-similar ordinary equations. Comprehensive parametric tests are conducted to determine the effects of the mixed convection parameter Ri, the magnetic parameter Mn and viscous dissipation parameter Ec on the local skin friction and local heat transfer are presented graphically and analyzed.