This work presents an unsteady analysis of the hydromagnetic flow of an exothermic fluid with thermal characteristics through a microchannel. Following the discretization of the partial differential equations, the modelled time-dependent governing equations are solved using the implicit finite-difference technique (IFDM). Graphs depicting the influence of key parameters are created, and the findings are thoroughly described. As the temperature rises due to the exothermic process, the buoyant force frequently overcomes the Darcy resistance. This creates a rise in fluid velocity, especially if the medium is highly permeable. The interconnecting ligaments (pores) significantly improve the fluid-solid contact area over a simple microchannel. Furthermore, it is discovered that varying thermal conductivity has a substantial impact on temperature and hydromagnetic fluid in the microchannel. This study's findings will benefit applications in biomedical and chemical engineering, including catalytic packed-bed reactors, bioreactors, and waste treatment. In these systems, the porous structure functions as both a flow regulator and a thermal stabilizer. Bio-microfluidic systems and heat management in microelectronics, where properties vary fast with temperature, can all benefit from the findings of this study.