In the present study, onset of stationary Benard-Marangoni convective instability in a fluid layer, with internal heating and thermally dependent viscosity has been investigated by means of linear stability analysis. The upper surface of a fluid layer is assumed to be deformably free and dependence of viscosity is assumed to be exponential. The resulting eigen value problem is solved using a regular perturbation technique with wave number a as a perturbation parameter. The viscosity parameter, surface deformation and the presence of internal heat source play a decisive role on the stability characteristics of the system. It is observed that both stabilizing and destabilizing factors can be enhanced because of the simultaneous presence of a volumetric heat source and variable viscosity so that a more precise control (suppress or augment) of Benard-Marangoni convective instability in a fluid layer is possible.