A Peltier cooler operates by converting electrical energy into thermal energy through the Peltier Effect, which involves the motion of electrons at a junction. When current is applied, electrons change their velocity based on the material's contact potential difference, leading to increased kinetic energy and heat generation. Conversely, when electrons slow down, they absorb heat, resulting in cooling. This process can be visualized by considering electron density variations in a metal rod under voltage, where hotter electrons migrate to areas of lower density. Overall, the Peltier junction effectively creates a temperature differential by manipulating electron movement.