This numerical study investigates natural convection and heat transfer in a closed chamber with porous medium. The system combines a porous layer and a Newtonian fluid with temperature-dependent viscosity, subjected to time-dependent thermal excitation. Governing equations, formulated in dimensionless stream function and vorticity variables, integrate mass, momentum, and energy conservation using the Darcy-Brinkman model and Boussinesq approximation. The LTNE framework resolves thermal decoupling between the porous matrix and fluid, overcoming limitations of local thermal equilibrium assumptions. A finite difference numerical scheme is employed to solve the dimensionless equations, analyzing the interplay of LTNE parameters (interphase heat transfer, parameters of solid structure) and periodic heating (frequency, amplitude). Results demonstrate that LTNE conditions significantly alter thermal stratification, velocity asymmetry, and heat transfer rates (with the help of the Nusselt number). Elevated heating frequencies suppress convective instabilities, while variable viscosity amplifies thermal gradients. The porous-fluid conductivity ratio critically modulates thermal non-equilibrium, with lower ratios exacerbating temperature disparities. This work validates the necessity of LTNE models for systems involving rapid thermal transients, heterogeneous media, or variable properties. The findings provide critical insights for optimizing thermal management in energy storage, electronic cooling, and geothermal systems.