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Cooling of heat-generating elements is a challenging problem in engineering. In this article, the transient free convection of a temperature-dependent viscosity liquid inside the porous cavity with copper radiator and the heat-generating element is studied using mathematical modeling techniques. The vertical and top walls of the chamber are kept at low constant temperature, while the bottom wall is kept adiabatic. The working fluid is a heat-conducting liquid with temperature-dependent viscosity. A mathematical model is developed based on dimensionless stream function, vorticity, and temperature variables. The governing properties are the variable viscosity, geometric parameters of the radiator, and size of thermally insulated strip on vertical surfaces of the cavity. The effect of these parameters on the energy transport and circulation patterns are analyzed numerically. Based on the numerical results obtained, recommendations are given on the optimal values of the governing parameters for the effective operation of the cooling system. It is shown that the optimal number of radiator fins for the cooling system configuration under consideration is 3. In addition, the thermal insulation of the vertical walls and the increased thickness of the radiator fins have a negative effect on the operation of the cooling system. [ABSTRACT FROM AUTHOR]