In the realm of thermal management for electronic systems, the efficacy of heat dissipation serves as a major predictor of the reliability and operational lifespan of electronic components. Simultaneously, within the realm of geothermal energy utilization, where harnessing the Earth’s inherent heat reservoirs is employed for power generation and direct heating applications, an intricate comprehension of temperature gradients and the dynamics governing heat transfer stands as an imperative prerequisite for optimizing the extraction of thermal energy. This work offers a complete mathematical model aimed at understanding the principles governing energy transfer inside naturally convected flows subjected to the impact of an external magnetic field. The analytical inspection involves a broad parametric study of the flow system, comprising variations in buoyancy-driven factors, as well as the magnetic field parameter, indicated as the Hartmann number (Ha), ranging from 0 to 50. This multifaceted study unveils the profound impact of magnetic fields on critical aspects of the flow, including isotherm alignment, velocity distributions, thereby paving the way for the development of advanced cooling systems poised to deliver elevated energy efficiency and enhanced performance in electronic devices. The computational analysis digs into the complicated temperature distributions, velocity profiles, and vorticity patterns. It is found that increment of the external magnetic force limits the variations in fluid’s horizontal and vertical velocities. Convective heat transfer is decreased with increasing Hartmann number at cold and hot sections of the fluid chamber. While for Rayleigh number this behavior is reversed.