Thermo-rheological effect of temperature-dependent viscous fluid saturating a porous medium has been studied in the presence of imposed time periodic gravity field and internal heat source. Weak nonlinear stability analysis has been performed by using the power series expansion in terms of the amplitude of gravity modulation, which is considered to be small. Nusselt number is calculated numerically using Ginzburg-Landau equation. The nonlinear effects of thermo-mechanical anisotropies, internal heat source parameter, Vadasz number, thermo-rheological parameter and amplitude of gravity modulation have been obtained and depicted graphically. Streamlines and isotherms have been drawn for different times. Comparisons have been made between various physical systems.