<p>The objective of this study is to analyze the Differential Cross Section (DCS) in a self-generated thermal environment (exothermic reaction) and laser field (generate due to deceleration/ retardation of electron in field of charged particle) around the electrode of a Proton Exchange Membrane Fuel Cell (PEMFC). To study this, a theoretical model was developed using the thermal Volkov wave function and the dressed ground-state wave function of hydrogen atoms within a self-generated non-monochromatic polarized laser field, incorporating the Byron and Joachain approximation for non-relativistic thermal potentials. The model evaluates DCS under varying polarization states (elliptical, circular and linear) and observation shows that elliptical polarization consistently produces the highest DCS during absorption, while linear polarization dominates in specific emission scenarios. Peaks in DCS result from constructive interference, whereas dip peaks are caused by destructive interference in non-monochromatic fields across various parameters. The study underscores the significant roles of molecular/atom oscillations, scattering angles, momentum changes, temperature, and phase relationships in influencing scattering. These findings have applications in optimizing laser-assisted processes, advancing spectroscopic techniques, improving quantum collision studies, quantum computing and measurement of temperature due to charged particle field interaction. Additionally, offer insights into enhancing PEMFC efficiency through thermal management and a deeper understanding of scattering mechanisms in complex thermal environments.</p>