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A numerical investigation of thermogravitational convection within porous cubical region under the non-uniform heating of vertical wall has been performed. The working liquid has a temperature-dependent viscosity according to exponential relation. Heat transmission inside porous structures has been described employing the local thermal non-equilibrium approach. The non-dimensional vector potential functions, vorticity vector and temperature have been added to formulate the mathematical model. The differential equations have been solved employing the second-order finite difference technique. The impact of key parameters on the fluid circulation structure and energy transfer within a cube has been investigated. These parameters include the Nield number, Darcy number, viscosity variation parameter and time. A presence of the porous layer leads to strengthening of the heat transfer. For high permeability properties of the porous medium (high Darcy numbers) and high values of the interfacial heat transfer coefficient (Nield number) the intensity of the flow in the cavity is raised. Additionally, using variable viscosity of the working liquid is also an effective way to manage the heat transfer and fluid flow.